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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 8976.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8976.h1 | 8976m3 | \([0, -1, 0, -265513088, 1665329197056]\) | \(505384091400037554067434625/815656731648\) | \(3340929972830208\) | \([2]\) | \(829440\) | \(3.1341\) | |
| 8976.h2 | 8976m4 | \([0, -1, 0, -265510528, 1665362913280]\) | \(-505369473241574671219626625/20303219722982711328\) | \(-83161987985337185599488\) | \([2]\) | \(1658880\) | \(3.4807\) | |
| 8976.h3 | 8976m1 | \([0, -1, 0, -3287168, 2271866880]\) | \(959024269496848362625/11151660319506432\) | \(45677200668698345472\) | \([2]\) | \(276480\) | \(2.5848\) | \(\Gamma_0(N)\)-optimal |
| 8976.h4 | 8976m2 | \([0, -1, 0, -665728, 5792985088]\) | \(-7966267523043306625/3534510366354604032\) | \(-14477354460588458115072\) | \([2]\) | \(552960\) | \(2.9314\) |
Rank
sage: E.rank()
The elliptic curves in class 8976.h have rank \(0\).
Complex multiplication
The elliptic curves in class 8976.h do not have complex multiplication.Modular form 8976.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
