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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 249090.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
249090.h1 | 249090h2 | \([1, 1, 0, -10478393, 15470053563]\) | \(-2704495231520617249/633724658718750\) | \(-29814134880847924968750\) | \([]\) | \(21772800\) | \(3.0317\) | |
249090.h2 | 249090h1 | \([1, 1, 0, 925597, -137798043]\) | \(1864091337486911/1254094471800\) | \(-58999979283060655800\) | \([]\) | \(7257600\) | \(2.4824\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 249090.h have rank \(0\).
Complex multiplication
The elliptic curves in class 249090.h do not have complex multiplication.Modular form 249090.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.