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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 152592.ch
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152592.ch1 | 152592cs1 | \([0, 1, 0, -378108, -89523348]\) | \(967473250000/1153977\) | \(7130675062249728\) | \([2]\) | \(1105920\) | \(1.9531\) | \(\Gamma_0(N)\)-optimal |
152592.ch2 | 152592cs2 | \([0, 1, 0, -279848, -137041884]\) | \(-98061470500/271048833\) | \(-6699478946720744448\) | \([2]\) | \(2211840\) | \(2.2997\) |
Rank
sage: E.rank()
The elliptic curves in class 152592.ch have rank \(0\).
Complex multiplication
The elliptic curves in class 152592.ch do not have complex multiplication.Modular form 152592.2.a.ch
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.