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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 3630h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3630.h2 | 3630h1 | \([1, 0, 1, -5129, -141748]\) | \(123286270205329/43200000\) | \(5227200000\) | \([]\) | \(4320\) | \(0.83502\) | \(\Gamma_0(N)\)-optimal |
3630.h1 | 3630h2 | \([1, 0, 1, -14369, 482876]\) | \(2711280982499089/732421875000\) | \(88623046875000\) | \([]\) | \(12960\) | \(1.3843\) |
Rank
sage: E.rank()
The elliptic curves in class 3630h have rank \(1\).
Complex multiplication
The elliptic curves in class 3630h do not have complex multiplication.Modular form 3630.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.