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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 3700.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3700.f1 | 3700c1 | \([0, -1, 0, -28, 72]\) | \(-393040/37\) | \(-236800\) | \([]\) | \(432\) | \(-0.22678\) | \(\Gamma_0(N)\)-optimal |
| 3700.f2 | 3700c2 | \([0, -1, 0, 172, -88]\) | \(87418160/50653\) | \(-324179200\) | \([]\) | \(1296\) | \(0.32253\) |
Rank
sage: E.rank()
The elliptic curves in class 3700.f have rank \(0\).
Complex multiplication
The elliptic curves in class 3700.f do not have complex multiplication.Modular form 3700.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
