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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1560c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1560.i3 | 1560c1 | \([0, 1, 0, -4876, 129440]\) | \(50091484483024/14625\) | \(3744000\) | \([2]\) | \(768\) | \(0.62742\) | \(\Gamma_0(N)\)-optimal |
1560.i2 | 1560c2 | \([0, 1, 0, -4896, 128304]\) | \(12677589459076/213890625\) | \(219024000000\) | \([2, 2]\) | \(1536\) | \(0.97399\) | |
1560.i1 | 1560c3 | \([0, 1, 0, -9896, -183696]\) | \(52337949619538/23423590125\) | \(47971512576000\) | \([2]\) | \(3072\) | \(1.3206\) | |
1560.i4 | 1560c4 | \([0, 1, 0, -216, 367920]\) | \(-546718898/28564453125\) | \(-58500000000000\) | \([2]\) | \(3072\) | \(1.3206\) |
Rank
sage: E.rank()
The elliptic curves in class 1560c have rank \(0\).
Complex multiplication
The elliptic curves in class 1560c do not have complex multiplication.Modular form 1560.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.