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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 69828c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
69828.l2 | 69828c1 | \([0, -1, 0, -49373, 4117638]\) | \(5619712000/184437\) | \(436852724151888\) | \([2]\) | \(304128\) | \(1.5826\) | \(\Gamma_0(N)\)-optimal |
69828.l1 | 69828c2 | \([0, -1, 0, -120788, -10422456]\) | \(5142706000/1728243\) | \(65495549161734912\) | \([2]\) | \(608256\) | \(1.9292\) |
Rank
sage: E.rank()
The elliptic curves in class 69828c have rank \(1\).
Complex multiplication
The elliptic curves in class 69828c do not have complex multiplication.Modular form 69828.2.a.c
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.