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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 418275.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
418275.bs1 | 418275bs1 | \([0, 0, 1, -887250, -337445469]\) | \(-56197120/3267\) | \(-4490521823119921875\) | \([]\) | \(6739200\) | \(2.3353\) | \(\Gamma_0(N)\)-optimal* |
418275.bs2 | 418275bs2 | \([0, 0, 1, 4816500, -596966094]\) | \(8990228480/5314683\) | \(-7305081112477641796875\) | \([]\) | \(20217600\) | \(2.8846\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 418275.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 418275.bs do not have complex multiplication.Modular form 418275.2.a.bs
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.