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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1568c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1568.h2 | 1568c1 | \([0, -1, 0, 82, 176]\) | \(8000/7\) | \(-52706752\) | \([2]\) | \(384\) | \(0.16918\) | \(\Gamma_0(N)\)-optimal |
1568.h1 | 1568c2 | \([0, -1, 0, -408, 1940]\) | \(125000/49\) | \(2951578112\) | \([2]\) | \(768\) | \(0.51575\) |
Rank
sage: E.rank()
The elliptic curves in class 1568c have rank \(0\).
Complex multiplication
The elliptic curves in class 1568c do not have complex multiplication.Modular form 1568.2.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.