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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 66880ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 66880.bn3 | 66880ce1 | \([0, 0, 0, -62874188, 191891924112]\) | \(104857852278310619039721/47155625\) | \(12361564160000\) | \([2]\) | \(2260992\) | \(2.7555\) | \(\Gamma_0(N)\)-optimal |
| 66880.bn2 | 66880ce2 | \([0, 0, 0, -62874508, 191889873168]\) | \(104859453317683374662841/2223652969140625\) | \(582917283942400000000\) | \([2, 2]\) | \(4521984\) | \(3.1021\) | |
| 66880.bn4 | 66880ce3 | \([0, 0, 0, -60679628, 205908132752]\) | \(-94256762600623910012361/15323275604248046875\) | \(-4016904760000000000000000\) | \([2]\) | \(9043968\) | \(3.4487\) | |
| 66880.bn1 | 66880ce4 | \([0, 0, 0, -65074508, 177740353168]\) | \(116256292809537371612841/15216540068579856875\) | \(3988924679737798000640000\) | \([2]\) | \(9043968\) | \(3.4487\) |
Rank
sage: E.rank()
The elliptic curves in class 66880ce have rank \(1\).
Complex multiplication
The elliptic curves in class 66880ce do not have complex multiplication.Modular form 66880.2.a.ce
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
