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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 1008.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1008.l1 | 1008k5 | \([0, 0, 0, -112899, -14601022]\) | \(53297461115137/147\) | \(438939648\) | \([2]\) | \(2048\) | \(1.3167\) | |
| 1008.l2 | 1008k3 | \([0, 0, 0, -7059, -227950]\) | \(13027640977/21609\) | \(64524128256\) | \([2, 2]\) | \(1024\) | \(0.97009\) | |
| 1008.l3 | 1008k4 | \([0, 0, 0, -5619, 161138]\) | \(6570725617/45927\) | \(137137287168\) | \([2]\) | \(1024\) | \(0.97009\) | |
| 1008.l4 | 1008k6 | \([0, 0, 0, -4899, -370078]\) | \(-4354703137/17294403\) | \(-51640810647552\) | \([4]\) | \(2048\) | \(1.3167\) | |
| 1008.l5 | 1008k2 | \([0, 0, 0, -579, -1150]\) | \(7189057/3969\) | \(11851370496\) | \([2, 2]\) | \(512\) | \(0.62351\) | |
| 1008.l6 | 1008k1 | \([0, 0, 0, 141, -142]\) | \(103823/63\) | \(-188116992\) | \([2]\) | \(256\) | \(0.27694\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1008.l have rank \(0\).
Complex multiplication
The elliptic curves in class 1008.l do not have complex multiplication.Modular form 1008.2.a.l
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
