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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 2646.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2646.h1 | 2646i1 | \([1, -1, 0, -8682, 320228]\) | \(-637875/16\) | \(-1815497249328\) | \([3]\) | \(6048\) | \(1.1366\) | \(\Gamma_0(N)\)-optimal |
2646.h2 | 2646i2 | \([1, -1, 0, 37623, 1329677]\) | \(5767125/4096\) | \(-4182905662451712\) | \([]\) | \(18144\) | \(1.6859\) |
Rank
sage: E.rank()
The elliptic curves in class 2646.h have rank \(0\).
Complex multiplication
The elliptic curves in class 2646.h do not have complex multiplication.Modular form 2646.2.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.