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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 59248.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59248.z1 | 59248bb6 | \([0, -1, 0, -23111128, -42756445200]\) | \(2251439055699625/25088\) | \(15212234273718272\) | \([2]\) | \(1824768\) | \(2.6740\) | |
| 59248.z2 | 59248bb5 | \([0, -1, 0, -1443288, -668832784]\) | \(-548347731625/1835008\) | \(-1112666278306250752\) | \([2]\) | \(912384\) | \(2.3274\) | |
| 59248.z3 | 59248bb4 | \([0, -1, 0, -300648, -51908752]\) | \(4956477625/941192\) | \(570696476424962048\) | \([2]\) | \(608256\) | \(2.1247\) | |
| 59248.z4 | 59248bb2 | \([0, -1, 0, -89048, 10250864]\) | \(128787625/98\) | \(59422790131712\) | \([2]\) | \(202752\) | \(1.5754\) | |
| 59248.z5 | 59248bb1 | \([0, -1, 0, -4408, 229488]\) | \(-15625/28\) | \(-16977940037632\) | \([2]\) | \(101376\) | \(1.2288\) | \(\Gamma_0(N)\)-optimal |
| 59248.z6 | 59248bb3 | \([0, -1, 0, 37912, -4781200]\) | \(9938375/21952\) | \(-13310704989503488\) | \([2]\) | \(304128\) | \(1.7781\) |
Rank
sage: E.rank()
The elliptic curves in class 59248.z have rank \(0\).
Complex multiplication
The elliptic curves in class 59248.z do not have complex multiplication.Modular form 59248.2.a.z
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
