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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 392d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 392.b2 | 392d1 | \([0, 1, 0, -16, 1392]\) | \(-4/7\) | \(-843308032\) | \([2]\) | \(192\) | \(0.39171\) | \(\Gamma_0(N)\)-optimal |
| 392.b1 | 392d2 | \([0, 1, 0, -1976, 32752]\) | \(3543122/49\) | \(11806312448\) | \([2]\) | \(384\) | \(0.73829\) |
Rank
sage: E.rank()
The elliptic curves in class 392d have rank \(0\).
Complex multiplication
The elliptic curves in class 392d do not have complex multiplication.Modular form 392.2.a.d
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 Cremona 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 Cremona labels.
