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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 21175s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 21175.v2 | 21175s1 | \([0, -1, 1, -100833, -852182]\) | \(6553600/3773\) | \(65274410673828125\) | \([]\) | \(129600\) | \(1.9160\) | \(\Gamma_0(N)\)-optimal |
| 21175.v1 | 21175s2 | \([0, -1, 1, -5394583, 4824400943]\) | \(1003555225600/9317\) | \(161187830439453125\) | \([]\) | \(388800\) | \(2.4653\) |
Rank
sage: E.rank()
The elliptic curves in class 21175s have rank \(1\).
Complex multiplication
The elliptic curves in class 21175s do not have complex multiplication.Modular form 21175.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
