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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 302330.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
302330.bb1 | 302330bb2 | \([1, -1, 1, -13375858, 18832480881]\) | \(2249574551450240063841/955072563200\) | \(112363331987916800\) | \([2]\) | \(9934848\) | \(2.6152\) | |
302330.bb2 | 302330bb1 | \([1, -1, 1, -831858, 297466481]\) | \(-541106281296959841/11321999360000\) | \(-1332021902704640000\) | \([2]\) | \(4967424\) | \(2.2686\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 302330.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 302330.bb do not have complex multiplication.Modular form 302330.2.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.