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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 7440.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7440.r1 | 7440s2 | \([0, 1, 0, -2576, -12780]\) | \(461710681489/252204840\) | \(1033031024640\) | \([2]\) | \(9216\) | \(0.99607\) | |
| 7440.r2 | 7440s1 | \([0, 1, 0, 624, -1260]\) | \(6549699311/4017600\) | \(-16456089600\) | \([2]\) | \(4608\) | \(0.64950\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7440.r have rank \(1\).
Complex multiplication
The elliptic curves in class 7440.r do not have complex multiplication.Modular form 7440.2.a.r
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
