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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 116380i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116380.h2 | 116380i1 | \([0, 0, 0, -2300092, 1819538349]\) | \(-568162198831104/275038671875\) | \(-651449508806318750000\) | \([2]\) | \(4561920\) | \(2.6994\) | \(\Gamma_0(N)\)-optimal |
116380.h1 | 116380i2 | \([0, 0, 0, -40321967, 98539583974]\) | \(191311845106276944/25466189375\) | \(965096955794042720000\) | \([2]\) | \(9123840\) | \(3.0459\) |
Rank
sage: E.rank()
The elliptic curves in class 116380i have rank \(1\).
Complex multiplication
The elliptic curves in class 116380i do not have complex multiplication.Modular form 116380.2.a.i
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.