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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 25392b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25392.i2 | 25392b1 | \([0, -1, 0, 8, -512]\) | \(4/9\) | \(-112131072\) | \([2]\) | \(9216\) | \(0.22355\) | \(\Gamma_0(N)\)-optimal |
25392.i1 | 25392b2 | \([0, -1, 0, -912, -10080]\) | \(3370318/81\) | \(2018359296\) | \([2]\) | \(18432\) | \(0.57013\) |
Rank
sage: E.rank()
The elliptic curves in class 25392b have rank \(0\).
Complex multiplication
The elliptic curves in class 25392b do not have complex multiplication.Modular form 25392.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.