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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 16800r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16800.be3 | 16800r1 | \([0, 1, 0, -159468758, 775053481488]\) | \(448487713888272974160064/91549016015625\) | \(91549016015625000000\) | \([2, 2]\) | \(2580480\) | \(3.2181\) | \(\Gamma_0(N)\)-optimal |
| 16800.be2 | 16800r2 | \([0, 1, 0, -160015633, 769469340863]\) | \(7079962908642659949376/100085966990454375\) | \(6405501887389080000000000\) | \([2]\) | \(5160960\) | \(3.5647\) | |
| 16800.be1 | 16800r3 | \([0, 1, 0, -2551500008, 49605979418988]\) | \(229625675762164624948320008/9568125\) | \(76545000000000\) | \([2]\) | \(5160960\) | \(3.5647\) | |
| 16800.be4 | 16800r4 | \([0, 1, 0, -158922008, 780632518488]\) | \(-55486311952875723077768/801237030029296875\) | \(-6409896240234375000000000\) | \([2]\) | \(5160960\) | \(3.5647\) |
Rank
sage: E.rank()
The elliptic curves in class 16800r have rank \(0\).
Complex multiplication
The elliptic curves in class 16800r do not have complex multiplication.Modular form 16800.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
