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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 37030h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37030.h2 | 37030h1 | \([1, -1, 0, -2692709, -1518102635]\) | \(1198785674367/140492800\) | \(253048980636388966400\) | \([2]\) | \(1483776\) | \(2.6465\) | \(\Gamma_0(N)\)-optimal |
37030.h1 | 37030h2 | \([1, -1, 0, -10479589, 11459511573]\) | \(70665260180607/9411920000\) | \(16952304757476838960000\) | \([2]\) | \(2967552\) | \(2.9931\) |
Rank
sage: E.rank()
The elliptic curves in class 37030h have rank \(1\).
Complex multiplication
The elliptic curves in class 37030h do not have complex multiplication.Modular form 37030.2.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.