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SageMath
E = EllipticCurve("fm1")
E.isogeny_class()
Elliptic curves in class 35280.fm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.fm1 | 35280cm2 | \([0, 0, 0, -105987, -9445534]\) | \(2185454/625\) | \(37654757763840000\) | \([2]\) | \(258048\) | \(1.8872\) | |
| 35280.fm2 | 35280cm1 | \([0, 0, 0, 17493, -974806]\) | \(19652/25\) | \(-753095155276800\) | \([2]\) | \(129024\) | \(1.5406\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35280.fm have rank \(0\).
Complex multiplication
The elliptic curves in class 35280.fm do not have complex multiplication.Modular form 35280.2.a.fm
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.
