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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 3870.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3870.g1 | 3870i2 | \([1, -1, 0, -1491984, 701818240]\) | \(503835593418244309249/898614000000\) | \(655089606000000\) | \([2]\) | \(80640\) | \(2.1013\) | |
3870.g2 | 3870i1 | \([1, -1, 0, -92304, 11216128]\) | \(-119305480789133569/5200091136000\) | \(-3790866438144000\) | \([2]\) | \(40320\) | \(1.7547\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3870.g have rank \(1\).
Complex multiplication
The elliptic curves in class 3870.g do not have complex multiplication.Modular form 3870.2.a.g
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.