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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 327990.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 327990.p1 | 327990p3 | \([1, 0, 1, -3554684153, 81569971645598]\) | \(8351005675201800382877041/395069604635949750\) | \(234996614255712626284119750\) | \([2]\) | \(348364800\) | \(4.1341\) | |
| 327990.p2 | 327990p4 | \([1, 0, 1, -1117886653, -13346698711402]\) | \(259734139401368855237041/20937966860481050250\) | \(12454390982939281967272880250\) | \([2]\) | \(348364800\) | \(4.1341\) | |
| 327990.p3 | 327990p2 | \([1, 0, 1, -233785403, 1133818842098]\) | \(2375679751819859057041/441134740310062500\) | \(262397231239703945967562500\) | \([2, 2]\) | \(174182400\) | \(3.7875\) | |
| 327990.p4 | 327990p1 | \([1, 0, 1, 29027097, 103278467098]\) | \(4547226203385942959/10377808593750000\) | \(-6172962572436714843750000\) | \([2]\) | \(87091200\) | \(3.4409\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 327990.p have rank \(0\).
Complex multiplication
The elliptic curves in class 327990.p do not have complex multiplication.Modular form 327990.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
