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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 116025c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116025.bh1 | 116025c1 | \([1, 1, 0, -11375, 462000]\) | \(10418796526321/6390657\) | \(99854015625\) | \([2]\) | \(179200\) | \(1.0534\) | \(\Gamma_0(N)\)-optimal |
116025.bh2 | 116025c2 | \([1, 1, 0, -9250, 642625]\) | \(-5602762882081/8312741073\) | \(-129886579265625\) | \([2]\) | \(358400\) | \(1.3999\) |
Rank
sage: E.rank()
The elliptic curves in class 116025c have rank \(1\).
Complex multiplication
The elliptic curves in class 116025c do not have complex multiplication.Modular form 116025.2.a.c
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.