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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 1680.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1680.t1 | 1680j5 | \([0, 1, 0, -10480, 409460]\) | \(62161150998242/1607445\) | \(3292047360\) | \([4]\) | \(2048\) | \(0.93291\) | |
| 1680.t2 | 1680j3 | \([0, 1, 0, -680, 5700]\) | \(34008619684/4862025\) | \(4978713600\) | \([2, 4]\) | \(1024\) | \(0.58634\) | |
| 1680.t3 | 1680j2 | \([0, 1, 0, -180, -900]\) | \(2533446736/275625\) | \(70560000\) | \([2, 2]\) | \(512\) | \(0.23977\) | |
| 1680.t4 | 1680j1 | \([0, 1, 0, -175, -952]\) | \(37256083456/525\) | \(8400\) | \([2]\) | \(256\) | \(-0.10681\) | \(\Gamma_0(N)\)-optimal |
| 1680.t5 | 1680j4 | \([0, 1, 0, 240, -4092]\) | \(1486779836/8203125\) | \(-8400000000\) | \([2]\) | \(1024\) | \(0.58634\) | |
| 1680.t6 | 1680j6 | \([0, 1, 0, 1120, 32340]\) | \(75798394558/259416045\) | \(-531284060160\) | \([4]\) | \(2048\) | \(0.93291\) |
Rank
sage: E.rank()
The elliptic curves in class 1680.t have rank \(0\).
Complex multiplication
The elliptic curves in class 1680.t do not have complex multiplication.Modular form 1680.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
