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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 103428.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 103428.bb1 | 103428j2 | \([0, 0, 0, -3729999, -2772723850]\) | \(6371214852688/77571\) | \(69875832904839936\) | \([2]\) | \(2322432\) | \(2.3805\) | |
| 103428.bb2 | 103428j1 | \([0, 0, 0, -239304, -40905943]\) | \(26919436288/2738853\) | \(154197150496738128\) | \([2]\) | \(1161216\) | \(2.0339\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 103428.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 103428.bb do not have complex multiplication.Modular form 103428.2.a.bb
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.
