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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 35600r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35600.z2 | 35600r1 | \([0, 1, 0, 2392, 228788]\) | \(23639903/364544\) | \(-23330816000000\) | \([]\) | \(82944\) | \(1.2457\) | \(\Gamma_0(N)\)-optimal |
| 35600.z1 | 35600r2 | \([0, 1, 0, -221608, 40100788]\) | \(-18806241149857/11279504\) | \(-721888256000000\) | \([]\) | \(248832\) | \(1.7950\) |
Rank
sage: E.rank()
The elliptic curves in class 35600r have rank \(0\).
Complex multiplication
The elliptic curves in class 35600r do not have complex multiplication.Modular form 35600.2.a.r
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.
