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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 65520.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 65520.p1 | 65520cm4 | \([0, 0, 0, -419403, 104543098]\) | \(2732315424539401/341250\) | \(1018967040000\) | \([2]\) | \(294912\) | \(1.7220\) | |
| 65520.p2 | 65520cm3 | \([0, 0, 0, -47883, -1429958]\) | \(4066120948681/2057248830\) | \(6142912090398720\) | \([2]\) | \(294912\) | \(1.7220\) | |
| 65520.p3 | 65520cm2 | \([0, 0, 0, -26283, 1624282]\) | \(672451615081/7452900\) | \(22254240153600\) | \([2, 2]\) | \(147456\) | \(1.3755\) | |
| 65520.p4 | 65520cm1 | \([0, 0, 0, -363, 63898]\) | \(-1771561/589680\) | \(-1760775045120\) | \([2]\) | \(73728\) | \(1.0289\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 65520.p have rank \(1\).
Complex multiplication
The elliptic curves in class 65520.p do not have complex multiplication.Modular form 65520.2.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.
