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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 18837.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18837.j1 | 18837q1 | \([0, 0, 1, -393186, -94895406]\) | \(-9221261135586623488/121324931\) | \(-88445874699\) | \([]\) | \(103680\) | \(1.6589\) | \(\Gamma_0(N)\)-optimal |
18837.j2 | 18837q2 | \([0, 0, 1, -370956, -106098507]\) | \(-7743965038771437568/2189290237869371\) | \(-1595992583406771459\) | \([3]\) | \(311040\) | \(2.2082\) |
Rank
sage: E.rank()
The elliptic curves in class 18837.j have rank \(1\).
Complex multiplication
The elliptic curves in class 18837.j do not have complex multiplication.Modular form 18837.2.a.j
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 LMFDB 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 LMFDB labels.