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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 376768n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 376768.n1 | 376768n1 | \([0, 1, 0, -24669, 461491]\) | \(2725888/1421\) | \(865529793680384\) | \([2]\) | \(1505280\) | \(1.5581\) | \(\Gamma_0(N)\)-optimal |
| 376768.n2 | 376768n2 | \([0, 1, 0, 93071, 3687567]\) | \(9148592/5887\) | \(-57372260609671168\) | \([2]\) | \(3010560\) | \(1.9046\) |
Rank
sage: E.rank()
The elliptic curves in class 376768n have rank \(1\).
Complex multiplication
The elliptic curves in class 376768n do not have complex multiplication.Modular form 376768.2.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.
