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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 57150.bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57150.bi1 | 57150bl2 | \([1, -1, 1, -5031248855, 137361737950647]\) | \(1236526859255318155975783969/38367061931916216\) | \(437024814818233147875000\) | \([]\) | \(28976640\) | \(4.0405\) | |
| 57150.bi2 | 57150bl1 | \([1, -1, 1, -22937855, -41879323353]\) | \(117174888570509216929/1273887851544576\) | \(14510378808999936000000\) | \([]\) | \(4139520\) | \(3.0675\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 57150.bi have rank \(1\).
Complex multiplication
The elliptic curves in class 57150.bi do not have complex multiplication.Modular form 57150.2.a.bi
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
