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SageMath
E = EllipticCurve("fv1")
E.isogeny_class()
Elliptic curves in class 92400.fv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.fv1 | 92400gk1 | \([0, 1, 0, -67408, 5655188]\) | \(529278808969/88704000\) | \(5677056000000000\) | \([2]\) | \(552960\) | \(1.7440\) | \(\Gamma_0(N)\)-optimal |
| 92400.fv2 | 92400gk2 | \([0, 1, 0, 124592, 32151188]\) | \(3342032927351/8893500000\) | \(-569184000000000000\) | \([2]\) | \(1105920\) | \(2.0906\) |
Rank
sage: E.rank()
The elliptic curves in class 92400.fv have rank \(0\).
Complex multiplication
The elliptic curves in class 92400.fv do not have complex multiplication.Modular form 92400.2.a.fv
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.
