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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 3520.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3520.p1 | 3520e4 | \([0, 0, 0, -3788, 89712]\) | \(22930509321/6875\) | \(1802240000\) | \([2]\) | \(2048\) | \(0.75406\) | |
| 3520.p2 | 3520e3 | \([0, 0, 0, -1868, -30352]\) | \(2749884201/73205\) | \(19190251520\) | \([2]\) | \(2048\) | \(0.75406\) | |
| 3520.p3 | 3520e2 | \([0, 0, 0, -268, 1008]\) | \(8120601/3025\) | \(792985600\) | \([2, 2]\) | \(1024\) | \(0.40748\) | |
| 3520.p4 | 3520e1 | \([0, 0, 0, 52, 112]\) | \(59319/55\) | \(-14417920\) | \([2]\) | \(512\) | \(0.060908\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3520.p have rank \(0\).
Complex multiplication
The elliptic curves in class 3520.p do not have complex multiplication.Modular form 3520.2.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.
