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SageMath
E = EllipticCurve("gu1")
E.isogeny_class()
Elliptic curves in class 348480.gu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348480.gu1 | 348480gu4 | \([0, 0, 0, -1088984028, 13831853432848]\) | \(6749703004355978704/5671875\) | \(120013535423232000000\) | \([2]\) | \(53084160\) | \(3.5884\) | |
| 348480.gu2 | 348480gu3 | \([0, 0, 0, -68046528, 216222557848]\) | \(-26348629355659264/24169921875\) | \(-31963832232750000000000\) | \([2]\) | \(26542080\) | \(3.2418\) | |
| 348480.gu3 | 348480gu2 | \([0, 0, 0, -13748988, 18068527312]\) | \(13584145739344/1195803675\) | \(25302501678694171852800\) | \([2]\) | \(17694720\) | \(3.0391\) | |
| 348480.gu4 | 348480gu1 | \([0, 0, 0, 952512, 1314697912]\) | \(72268906496/606436875\) | \(-801990450465747840000\) | \([2]\) | \(8847360\) | \(2.6925\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 348480.gu have rank \(0\).
Complex multiplication
The elliptic curves in class 348480.gu do not have complex multiplication.Modular form 348480.2.a.gu
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
