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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 9702.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9702.h1 | 9702h1 | \([1, -1, 0, -11328, 177344]\) | \(69426531/34496\) | \(79881878970432\) | \([2]\) | \(27648\) | \(1.3606\) | \(\Gamma_0(N)\)-optimal |
9702.h2 | 9702h2 | \([1, -1, 0, 41592, 1331000]\) | \(3436115229/2324168\) | \(-5382041595632856\) | \([2]\) | \(55296\) | \(1.7072\) |
Rank
sage: E.rank()
The elliptic curves in class 9702.h have rank \(0\).
Complex multiplication
The elliptic curves in class 9702.h do not have complex multiplication.Modular form 9702.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.