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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 25350.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25350.h1 | 25350v2 | \([1, 1, 0, -7075, -234125]\) | \(-45646645/486\) | \(-417086718750\) | \([]\) | \(36000\) | \(1.0462\) | |
25350.h2 | 25350v1 | \([1, 1, 0, 75, 525]\) | \(33275/96\) | \(-131820000\) | \([]\) | \(7200\) | \(0.24153\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25350.h have rank \(1\).
Complex multiplication
The elliptic curves in class 25350.h do not have complex multiplication.Modular form 25350.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.