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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 26520.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26520.h1 | 26520p4 | \([0, -1, 0, -9929296, -12039444404]\) | \(52862679907533400952738/90903515625\) | \(186170400000000\) | \([2]\) | \(720896\) | \(2.4270\) | |
| 26520.h2 | 26520p2 | \([0, -1, 0, -620776, -187836740]\) | \(25836234020391349156/33847087730625\) | \(34659417836160000\) | \([2, 2]\) | \(360448\) | \(2.0805\) | |
| 26520.h3 | 26520p3 | \([0, -1, 0, -451776, -292549140]\) | \(-4979252943420552578/15190164405108225\) | \(-31109456701661644800\) | \([2]\) | \(720896\) | \(2.4270\) | |
| 26520.h4 | 26520p1 | \([0, -1, 0, -49556, -1162044]\) | \(52575237512036944/28081530070425\) | \(7188871698028800\) | \([4]\) | \(180224\) | \(1.7339\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 26520.h have rank \(0\).
Complex multiplication
The elliptic curves in class 26520.h do not have complex multiplication.Modular form 26520.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
