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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 20286.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20286.s1 | 20286s2 | \([1, -1, 0, -3028797, 2029623133]\) | \(104453838382375/14904\) | \(438442585712712\) | \([2]\) | \(258048\) | \(2.2192\) | |
| 20286.s2 | 20286s1 | \([1, -1, 0, -188757, 31938997]\) | \(-25282750375/304704\) | \(-8963715085682112\) | \([2]\) | \(129024\) | \(1.8727\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20286.s have rank \(1\).
Complex multiplication
The elliptic curves in class 20286.s do not have complex multiplication.Modular form 20286.2.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.
