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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 10780b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10780.b1 | 10780b1 | \([0, 1, 0, -1486, 21825]\) | \(-3937024/55\) | \(-5073024880\) | \([3]\) | \(9072\) | \(0.66825\) | \(\Gamma_0(N)\)-optimal |
| 10780.b2 | 10780b2 | \([0, 1, 0, 5374, 113749]\) | \(186050816/166375\) | \(-15345900262000\) | \([]\) | \(27216\) | \(1.2176\) |
Rank
sage: E.rank()
The elliptic curves in class 10780b have rank \(0\).
Complex multiplication
The elliptic curves in class 10780b do not have complex multiplication.Modular form 10780.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
