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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 2520.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2520.f1 | 2520e5 | \([0, 0, 0, -94323, 11149742]\) | \(62161150998242/1607445\) | \(2399902525440\) | \([2]\) | \(8192\) | \(1.4822\) | |
| 2520.f2 | 2520e3 | \([0, 0, 0, -6123, 160022]\) | \(34008619684/4862025\) | \(3629482214400\) | \([2, 2]\) | \(4096\) | \(1.1356\) | |
| 2520.f3 | 2520e2 | \([0, 0, 0, -1623, -22678]\) | \(2533446736/275625\) | \(51438240000\) | \([2, 2]\) | \(2048\) | \(0.78907\) | |
| 2520.f4 | 2520e1 | \([0, 0, 0, -1578, -24127]\) | \(37256083456/525\) | \(6123600\) | \([2]\) | \(1024\) | \(0.44250\) | \(\Gamma_0(N)\)-optimal |
| 2520.f5 | 2520e4 | \([0, 0, 0, 2157, -112642]\) | \(1486779836/8203125\) | \(-6123600000000\) | \([2]\) | \(4096\) | \(1.1356\) | |
| 2520.f6 | 2520e6 | \([0, 0, 0, 10077, 863102]\) | \(75798394558/259416045\) | \(-387306079856640\) | \([2]\) | \(8192\) | \(1.4822\) |
Rank
sage: E.rank()
The elliptic curves in class 2520.f have rank \(0\).
Complex multiplication
The elliptic curves in class 2520.f do not have complex multiplication.Modular form 2520.2.a.f
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
