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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 7440u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7440.q3 | 7440u1 | \([0, 1, 0, -1736, 24180]\) | \(141339344329/17141760\) | \(70212648960\) | \([2]\) | \(6912\) | \(0.81173\) | \(\Gamma_0(N)\)-optimal |
| 7440.q2 | 7440u2 | \([0, 1, 0, -6856, -194956]\) | \(8702409880009/1120910400\) | \(4591248998400\) | \([2, 2]\) | \(13824\) | \(1.1583\) | |
| 7440.q1 | 7440u3 | \([0, 1, 0, -106056, -13329036]\) | \(32208729120020809/658986840\) | \(2699210096640\) | \([2]\) | \(27648\) | \(1.5049\) | |
| 7440.q4 | 7440u4 | \([0, 1, 0, 10424, -1003660]\) | \(30579142915511/124675335000\) | \(-510670172160000\) | \([2]\) | \(27648\) | \(1.5049\) |
Rank
sage: E.rank()
The elliptic curves in class 7440u have rank \(0\).
Complex multiplication
The elliptic curves in class 7440u do not have complex multiplication.Modular form 7440.2.a.u
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 Cremona 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 Cremona labels.
