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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 7440n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7440.g2 | 7440n1 | \([0, -1, 0, -218360, -39258000]\) | \(-281115640967896441/468084326400\) | \(-1917273400934400\) | \([2]\) | \(49920\) | \(1.8283\) | \(\Gamma_0(N)\)-optimal |
| 7440.g1 | 7440n2 | \([0, -1, 0, -3495160, -2513897360]\) | \(1152829477932246539641/3188367360\) | \(13059552706560\) | \([2]\) | \(99840\) | \(2.1749\) |
Rank
sage: E.rank()
The elliptic curves in class 7440n have rank \(1\).
Complex multiplication
The elliptic curves in class 7440n do not have complex multiplication.Modular form 7440.2.a.n
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
