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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 15631b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15631.b1 | 15631b1 | \([0, -1, 1, -3103, -99233]\) | \(-28094464000/20657483\) | \(-2430332217467\) | \([]\) | \(16128\) | \(1.0760\) | \(\Gamma_0(N)\)-optimal |
15631.b2 | 15631b2 | \([0, -1, 1, 25317, 1539180]\) | \(15252992000000/17621717267\) | \(-2073177414745283\) | \([]\) | \(48384\) | \(1.6253\) |
Rank
sage: E.rank()
The elliptic curves in class 15631b have rank \(1\).
Complex multiplication
The elliptic curves in class 15631b do not have complex multiplication.Modular form 15631.2.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 Cremona 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 Cremona labels.