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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 5577c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5577.f2 | 5577c1 | \([1, 1, 0, 335, 3112]\) | \(857375/1287\) | \(-6212103183\) | \([2]\) | \(2688\) | \(0.56454\) | \(\Gamma_0(N)\)-optimal |
5577.f1 | 5577c2 | \([1, 1, 0, -2200, 28969]\) | \(244140625/61347\) | \(296110251723\) | \([2]\) | \(5376\) | \(0.91111\) |
Rank
sage: E.rank()
The elliptic curves in class 5577c have rank \(1\).
Complex multiplication
The elliptic curves in class 5577c do not have complex multiplication.Modular form 5577.2.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.