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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 57960i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57960.l2 | 57960i1 | \([0, 0, 0, -18892443, 31581682918]\) | \(998988730325355742564/917843977003905\) | \(685166857457507066880\) | \([2]\) | \(3379200\) | \(2.9214\) | \(\Gamma_0(N)\)-optimal |
| 57960.l1 | 57960i2 | \([0, 0, 0, -23272563, 15840407662]\) | \(933681761518863863522/467721356521811175\) | \(698304243516211909785600\) | \([2]\) | \(6758400\) | \(3.2680\) |
Rank
sage: E.rank()
The elliptic curves in class 57960i have rank \(0\).
Complex multiplication
The elliptic curves in class 57960i do not have complex multiplication.Modular form 57960.2.a.i
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
