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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 380880.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 380880.bn1 | 380880bn2 | \([0, 0, 0, -59875923, 123508847378]\) | \(53706380371489/16171875000\) | \(7148499122485440000000000\) | \([2]\) | \(48660480\) | \(3.4743\) | |
| 380880.bn2 | 380880bn1 | \([0, 0, 0, 10205997, 12933594002]\) | \(265971760991/317400000\) | \(-140301209443980902400000\) | \([2]\) | \(24330240\) | \(3.1277\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 380880.bn have rank \(0\).
Complex multiplication
The elliptic curves in class 380880.bn do not have complex multiplication.Modular form 380880.2.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 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.
