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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 19600.cs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19600.cs1 | 19600dr2 | \([0, 1, 0, -3329328, 2337097748]\) | \(-162677523113838677\) | \(-25088000\) | \([]\) | \(113664\) | \(1.9636\) | |
19600.cs2 | 19600dr1 | \([0, 1, 0, -128, -652]\) | \(-9317\) | \(-25088000\) | \([]\) | \(3072\) | \(0.15817\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19600.cs have rank \(0\).
Complex multiplication
The elliptic curves in class 19600.cs do not have complex multiplication.Modular form 19600.2.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.
\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.