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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1083a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1083.c2 | 1083a1 | \([1, 1, 0, 715, 8292]\) | \(2375/3\) | \(-50950689123\) | \([]\) | \(684\) | \(0.74052\) | \(\Gamma_0(N)\)-optimal |
1083.c1 | 1083a2 | \([1, 1, 0, -239350, -45171941]\) | \(-89289015625/2187\) | \(-37143052370667\) | \([]\) | \(4788\) | \(1.7135\) |
Rank
sage: E.rank()
The elliptic curves in class 1083a have rank \(1\).
Complex multiplication
The elliptic curves in class 1083a do not have complex multiplication.Modular form 1083.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.