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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 6930.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6930.be1 | 6930bf1 | \([1, -1, 1, -1517, 19541]\) | \(529278808969/88704000\) | \(64665216000\) | \([2]\) | \(7680\) | \(0.79544\) | \(\Gamma_0(N)\)-optimal |
| 6930.be2 | 6930bf2 | \([1, -1, 1, 2803, 107669]\) | \(3342032927351/8893500000\) | \(-6483361500000\) | \([2]\) | \(15360\) | \(1.1420\) |
Rank
sage: E.rank()
The elliptic curves in class 6930.be have rank \(1\).
Complex multiplication
The elliptic curves in class 6930.be do not have complex multiplication.Modular form 6930.2.a.be
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.
