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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 58800.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58800.b1 | 58800gr2 | \([0, -1, 0, -2813100208, 57429232078912]\) | \(266916252066900625/162\) | \(1494236419200000000\) | \([]\) | \(21772800\) | \(3.7100\) | |
58800.b2 | 58800gr1 | \([0, -1, 0, -34800208, 78452158912]\) | \(505318200625/4251528\) | \(39214740585484800000000\) | \([]\) | \(7257600\) | \(3.1607\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 58800.b have rank \(1\).
Complex multiplication
The elliptic curves in class 58800.b do not have complex multiplication.Modular form 58800.2.a.b
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.