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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 202860s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 202860.ct1 | 202860s1 | \([0, 0, 0, -1161069357, 15227736687569]\) | \(-126142795384287538429696/9315359375\) | \(-12783075829035750000\) | \([]\) | \(51010560\) | \(3.5625\) | \(\Gamma_0(N)\)-optimal |
| 202860.ct2 | 202860s2 | \([0, 0, 0, -1149382857, 15549282929369]\) | \(-122372013839654770813696/5297595236711512175\) | \(-7269667105293171124704370800\) | \([]\) | \(153031680\) | \(4.1118\) |
Rank
sage: E.rank()
The elliptic curves in class 202860s have rank \(0\).
Complex multiplication
The elliptic curves in class 202860s do not have complex multiplication.Modular form 202860.2.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.
