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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 58080.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58080.f1 | 58080bg4 | \([0, -1, 0, -384336, -91579464]\) | \(6922005943112/185625\) | \(168369157440000\) | \([2]\) | \(368640\) | \(1.8345\) | |
| 58080.f2 | 58080bg3 | \([0, -1, 0, -106641, 12137985]\) | \(18483505984/1976535\) | \(14342358307368960\) | \([2]\) | \(368640\) | \(1.8345\) | |
| 58080.f3 | 58080bg1 | \([0, -1, 0, -24966, -1305720]\) | \(15179306176/2205225\) | \(250028198798400\) | \([2, 2]\) | \(184320\) | \(1.4879\) | \(\Gamma_0(N)\)-optimal |
| 58080.f4 | 58080bg2 | \([0, -1, 0, 41584, -7135500]\) | \(8767302328/29229255\) | \(-26512081007132160\) | \([2]\) | \(368640\) | \(1.8345\) |
Rank
sage: E.rank()
The elliptic curves in class 58080.f have rank \(1\).
Complex multiplication
The elliptic curves in class 58080.f do not have complex multiplication.Modular form 58080.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
