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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 2320.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2320.f1 | 2320d3 | \([0, 0, 0, -827, 7546]\) | \(61085802564/11328125\) | \(11600000000\) | \([4]\) | \(1024\) | \(0.64940\) | |
| 2320.f2 | 2320d2 | \([0, 0, 0, -247, -1386]\) | \(6509904336/525625\) | \(134560000\) | \([2, 2]\) | \(512\) | \(0.30283\) | |
| 2320.f3 | 2320d1 | \([0, 0, 0, -242, -1449]\) | \(97960237056/725\) | \(11600\) | \([2]\) | \(256\) | \(-0.043745\) | \(\Gamma_0(N)\)-optimal |
| 2320.f4 | 2320d4 | \([0, 0, 0, 253, -6286]\) | \(1748981916/17682025\) | \(-18106393600\) | \([4]\) | \(1024\) | \(0.64940\) |
Rank
sage: E.rank()
The elliptic curves in class 2320.f have rank \(1\).
Complex multiplication
The elliptic curves in class 2320.f do not have complex multiplication.Modular form 2320.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
