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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 2110h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2110.e1 | 2110h1 | \([1, -1, 1, -10422, 412869]\) | \(-125180837135497521/270080000000\) | \(-270080000000\) | \([7]\) | \(5600\) | \(1.0776\) | \(\Gamma_0(N)\)-optimal |
2110.e2 | 2110h2 | \([1, -1, 1, 12678, -29358411]\) | \(225376208668020879/372397865250251420\) | \(-372397865250251420\) | \([]\) | \(39200\) | \(2.0505\) |
Rank
sage: E.rank()
The elliptic curves in class 2110h have rank \(0\).
Complex multiplication
The elliptic curves in class 2110h do not have complex multiplication.Modular form 2110.2.a.h
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.