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SageMath
E = EllipticCurve("fa1")
E.isogeny_class()
Elliptic curves in class 215600.fa
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 215600.fa1 | 215600cn1 | \([0, 0, 0, -7637875, -8122668750]\) | \(52355598021/15092\) | \(14204469664000000000\) | \([2]\) | \(6635520\) | \(2.6550\) | \(\Gamma_0(N)\)-optimal |
| 215600.fa2 | 215600cn2 | \([0, 0, 0, -6657875, -10283568750]\) | \(-34677868581/28471058\) | \(-26796732021136000000000\) | \([2]\) | \(13271040\) | \(3.0016\) |
Rank
sage: E.rank()
The elliptic curves in class 215600.fa have rank \(1\).
Complex multiplication
The elliptic curves in class 215600.fa do not have complex multiplication.Modular form 215600.2.a.fa
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
