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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 7920bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7920.d2 | 7920bd1 | \([0, 0, 0, 1437, -84638]\) | \(109902239/1100000\) | \(-3284582400000\) | \([]\) | \(14400\) | \(1.0828\) | \(\Gamma_0(N)\)-optimal |
| 7920.d1 | 7920bd2 | \([0, 0, 0, -855363, -304490558]\) | \(-23178622194826561/1610510\) | \(-4808957091840\) | \([]\) | \(72000\) | \(1.8875\) |
Rank
sage: E.rank()
The elliptic curves in class 7920bd have rank \(0\).
Complex multiplication
The elliptic curves in class 7920bd do not have complex multiplication.Modular form 7920.2.a.bd
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
