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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 152880.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152880.g1 | 152880ed8 | \([0, -1, 0, -7226927696, -236335272277824]\) | \(86623684689189325642735681/56690726941459561860\) | \(27318711639800938468422205440\) | \([2]\) | \(150994944\) | \(4.3961\) | |
| 152880.g2 | 152880ed3 | \([0, -1, 0, -4383375376, 111703502257600]\) | \(19328649688935739391016961/1048320\) | \(505175243489280\) | \([2]\) | \(37748736\) | \(3.7030\) | |
| 152880.g3 | 152880ed6 | \([0, -1, 0, -539956496, -2146841699904]\) | \(36128658497509929012481/16775330746084419600\) | \(8083869232931167770707558400\) | \([2, 2]\) | \(75497472\) | \(4.0495\) | |
| 152880.g4 | 152880ed4 | \([0, -1, 0, -274964496, 1732005199296]\) | \(4770955732122964500481/71987251059360000\) | \(34689958297119312445440000\) | \([2, 2]\) | \(37748736\) | \(3.7030\) | |
| 152880.g5 | 152880ed2 | \([0, -1, 0, -273960976, 1745435508160]\) | \(4718909406724749250561/1098974822400\) | \(529585311254682009600\) | \([2, 2]\) | \(18874368\) | \(3.3564\) | |
| 152880.g6 | 152880ed5 | \([0, -1, 0, -26028816, 4751296274880]\) | \(-4047051964543660801/20235220197806250000\) | \(-9751156412627793945600000000\) | \([2]\) | \(75497472\) | \(4.0495\) | |
| 152880.g7 | 152880ed1 | \([0, -1, 0, -17059856, 27486338496]\) | \(-1139466686381936641/17587891077120\) | \(-8475434177872244244480\) | \([2]\) | \(9437184\) | \(3.0098\) | \(\Gamma_0(N)\)-optimal |
| 152880.g8 | 152880ed7 | \([0, -1, 0, 1907142704, -16208852542784]\) | \(1591934139020114746758719/1156766383092650262660\) | \(-557434504005497695238907248640\) | \([2]\) | \(150994944\) | \(4.3961\) |
Rank
sage: E.rank()
The elliptic curves in class 152880.g have rank \(1\).
Complex multiplication
The elliptic curves in class 152880.g do not have complex multiplication.Modular form 152880.2.a.g
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 2 & 4 & 8 & 8 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 2 & 8 & 1 & 2 & 4 & 4 & 8 & 2 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 8 & 8 & 4 & 2 & 4 & 1 & 8 & 8 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 2 & 4 & 8 & 8 & 16 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
