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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 9025.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9025.b1 | 9025f2 | \([0, 0, 1, -849658625, 9532675710156]\) | \(2045023375454208\) | \(33171021564453125\) | \([]\) | \(1778400\) | \(3.4077\) | |
9025.b2 | 9025f1 | \([0, 0, 1, -857375, -305439844]\) | \(2101248\) | \(33171021564453125\) | \([]\) | \(136800\) | \(2.1252\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9025.b have rank \(0\).
Complex multiplication
The elliptic curves in class 9025.b do not have complex multiplication.Modular form 9025.2.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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.