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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 496860cs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
496860.cs2 | 496860cs1 | \([0, 1, 0, -105681, 12831300]\) | \(4927700992/151875\) | \(4023097033410000\) | \([2]\) | \(4515840\) | \(1.7699\) | \(\Gamma_0(N)\)-optimal |
496860.cs1 | 496860cs2 | \([0, 1, 0, -253556, -31176300]\) | \(4253563312/1476225\) | \(625672050635923200\) | \([2]\) | \(9031680\) | \(2.1164\) |
Rank
sage: E.rank()
The elliptic curves in class 496860cs have rank \(0\).
Complex multiplication
The elliptic curves in class 496860cs do not have complex multiplication.Modular form 496860.2.a.cs
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.