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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 123840bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 123840.s2 | 123840bn1 | \([0, 0, 0, -2028, -29648]\) | \(19307236/3225\) | \(154076774400\) | \([2]\) | \(114688\) | \(0.86789\) | \(\Gamma_0(N)\)-optimal |
| 123840.s1 | 123840bn2 | \([0, 0, 0, -9228, 313072]\) | \(909513218/83205\) | \(7950361559040\) | \([2]\) | \(229376\) | \(1.2145\) |
Rank
sage: E.rank()
The elliptic curves in class 123840bn have rank \(2\).
Complex multiplication
The elliptic curves in class 123840bn do not have complex multiplication.Modular form 123840.2.a.bn
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.
