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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 42350bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42350.x2 | 42350bh1 | \([1, -1, 0, -28397, -6126939]\) | \(-11436248277/66784256\) | \(-14789047917952000\) | \([2]\) | \(230400\) | \(1.7865\) | \(\Gamma_0(N)\)-optimal |
42350.x1 | 42350bh2 | \([1, -1, 0, -705997, -227702139]\) | \(175738332394197/396829664\) | \(87875994548188000\) | \([2]\) | \(460800\) | \(2.1331\) |
Rank
sage: E.rank()
The elliptic curves in class 42350bh have rank \(1\).
Complex multiplication
The elliptic curves in class 42350bh do not have complex multiplication.Modular form 42350.2.a.bh
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 Cremona 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 Cremona labels.