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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 13200.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13200.t1 | 13200h3 | \([0, -1, 0, -1320008, -583291488]\) | \(15897679904620804/2475\) | \(39600000000\) | \([2]\) | \(98304\) | \(1.8801\) | |
| 13200.t2 | 13200h5 | \([0, -1, 0, -700008, 221338512]\) | \(1185450336504002/26043266205\) | \(833384518560000000\) | \([2]\) | \(196608\) | \(2.2267\) | |
| 13200.t3 | 13200h4 | \([0, -1, 0, -95008, -6141488]\) | \(5927735656804/2401490025\) | \(38423840400000000\) | \([2, 2]\) | \(98304\) | \(1.8801\) | |
| 13200.t4 | 13200h2 | \([0, -1, 0, -82508, -9091488]\) | \(15529488955216/6125625\) | \(24502500000000\) | \([2, 2]\) | \(49152\) | \(1.5335\) | |
| 13200.t5 | 13200h1 | \([0, -1, 0, -4383, -185238]\) | \(-37256083456/38671875\) | \(-9667968750000\) | \([2]\) | \(24576\) | \(1.1870\) | \(\Gamma_0(N)\)-optimal |
| 13200.t6 | 13200h6 | \([0, -1, 0, 309992, -45021488]\) | \(102949393183198/86815346805\) | \(-2778091097760000000\) | \([2]\) | \(196608\) | \(2.2267\) |
Rank
sage: E.rank()
The elliptic curves in class 13200.t have rank \(0\).
Complex multiplication
The elliptic curves in class 13200.t do not have complex multiplication.Modular form 13200.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
