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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 36225.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 36225.r1 | 36225bp4 | \([1, -1, 1, -1136480, -466035478]\) | \(14251520160844849/264449745\) | \(3012247876640625\) | \([2]\) | \(368640\) | \(2.0951\) | |
| 36225.r2 | 36225bp2 | \([1, -1, 1, -73355, -6765478]\) | \(3832302404449/472410225\) | \(5381047719140625\) | \([2, 2]\) | \(184320\) | \(1.7485\) | |
| 36225.r3 | 36225bp1 | \([1, -1, 1, -18230, 841772]\) | \(58818484369/7455105\) | \(84918305390625\) | \([4]\) | \(92160\) | \(1.4019\) | \(\Gamma_0(N)\)-optimal |
| 36225.r4 | 36225bp3 | \([1, -1, 1, 107770, -35020978]\) | \(12152722588271/53476250625\) | \(-609127917275390625\) | \([2]\) | \(368640\) | \(2.0951\) |
Rank
sage: E.rank()
The elliptic curves in class 36225.r have rank \(1\).
Complex multiplication
The elliptic curves in class 36225.r do not have complex multiplication.Modular form 36225.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
