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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 238260.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 238260.n1 | 238260n2 | \([0, 1, 0, -11146356, 13018041684]\) | \(12716304220387024/1276763087655\) | \(15377009737474482958080\) | \([2]\) | \(27371520\) | \(2.9935\) | |
| 238260.n2 | 238260n1 | \([0, 1, 0, 865919, 986547044]\) | \(95392323977216/613447285275\) | \(-461762687725131236400\) | \([2]\) | \(13685760\) | \(2.6469\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 238260.n have rank \(1\).
Complex multiplication
The elliptic curves in class 238260.n do not have complex multiplication.Modular form 238260.2.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 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.
