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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 5082.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5082.s1 | 5082t2 | \([1, 1, 1, -12768, 523227]\) | \(129938649625/7072758\) | \(12529822235238\) | \([2]\) | \(15360\) | \(1.2692\) | |
| 5082.s2 | 5082t1 | \([1, 1, 1, 542, 33419]\) | \(9938375/274428\) | \(-486165942108\) | \([2]\) | \(7680\) | \(0.92258\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5082.s have rank \(0\).
Complex multiplication
The elliptic curves in class 5082.s do not have complex multiplication.Modular form 5082.2.a.s
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.
