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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 1170h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1170.l2 | 1170h1 | \([1, -1, 1, 151252, -13465169]\) | \(19441890357117957/15208161280000\) | \(-299342238474240000\) | \([2]\) | \(15360\) | \(2.0414\) | \(\Gamma_0(N)\)-optimal |
1170.l1 | 1170h2 | \([1, -1, 1, -712748, -115762769]\) | \(2034416504287874043/882294347833600\) | \(17366199648408748800\) | \([2]\) | \(30720\) | \(2.3879\) |
Rank
sage: E.rank()
The elliptic curves in class 1170h have rank \(0\).
Complex multiplication
The elliptic curves in class 1170h do not have complex multiplication.Modular form 1170.2.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 Cremona 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 Cremona labels.