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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 103056.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 103056.bd1 | 103056i1 | \([0, 1, 0, -1388, -19476]\) | \(1156019074000/58954473\) | \(15092345088\) | \([2]\) | \(78080\) | \(0.71121\) | \(\Gamma_0(N)\)-optimal |
| 103056.bd2 | 103056i2 | \([0, 1, 0, 872, -74620]\) | \(71527833500/2408785857\) | \(-2466596717568\) | \([2]\) | \(156160\) | \(1.0578\) |
Rank
sage: E.rank()
The elliptic curves in class 103056.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 103056.bd do not have complex multiplication.Modular form 103056.2.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 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.
