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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 494190.cs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
494190.cs1 | 494190cs2 | \([1, -1, 0, -1408929, -637147747]\) | \(651038076963/7220000\) | \(3430220343926940000\) | \([2]\) | \(18923520\) | \(2.3709\) | |
494190.cs2 | 494190cs1 | \([1, -1, 0, -160449, 8815805]\) | \(961504803/486400\) | \(231088528432972800\) | \([2]\) | \(9461760\) | \(2.0243\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 494190.cs have rank \(0\).
Complex multiplication
The elliptic curves in class 494190.cs do not have complex multiplication.Modular form 494190.2.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 LMFDB 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 LMFDB labels.