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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 3600.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3600.t1 | 3600l5 | \([0, 0, 0, -720075, -235187750]\) | \(1770025017602/75\) | \(1749600000000\) | \([2]\) | \(24576\) | \(1.8340\) | |
| 3600.t2 | 3600l3 | \([0, 0, 0, -45075, -3662750]\) | \(868327204/5625\) | \(65610000000000\) | \([2, 2]\) | \(12288\) | \(1.4874\) | |
| 3600.t3 | 3600l6 | \([0, 0, 0, -18075, -8009750]\) | \(-27995042/1171875\) | \(-27337500000000000\) | \([2]\) | \(24576\) | \(1.8340\) | |
| 3600.t4 | 3600l2 | \([0, 0, 0, -4575, 22750]\) | \(3631696/2025\) | \(5904900000000\) | \([2, 2]\) | \(6144\) | \(1.1409\) | |
| 3600.t5 | 3600l1 | \([0, 0, 0, -3450, 77875]\) | \(24918016/45\) | \(8201250000\) | \([2]\) | \(3072\) | \(0.79430\) | \(\Gamma_0(N)\)-optimal |
| 3600.t6 | 3600l4 | \([0, 0, 0, 17925, 180250]\) | \(54607676/32805\) | \(-382637520000000\) | \([2]\) | \(12288\) | \(1.4874\) |
Rank
sage: E.rank()
The elliptic curves in class 3600.t have rank \(0\).
Complex multiplication
The elliptic curves in class 3600.t do not have complex multiplication.Modular form 3600.2.a.t
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
