Show commands:
SageMath
E = EllipticCurve("el1")
E.isogeny_class()
Elliptic curves in class 206400el
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 206400.cp3 | 206400el1 | \([0, -1, 0, -537533, -151510563]\) | \(1073544204384256/16125\) | \(258000000000\) | \([2]\) | \(884736\) | \(1.7397\) | \(\Gamma_0(N)\)-optimal |
| 206400.cp2 | 206400el2 | \([0, -1, 0, -538033, -151214063]\) | \(67283921459536/260015625\) | \(66564000000000000\) | \([2, 2]\) | \(1769472\) | \(2.0863\) | |
| 206400.cp1 | 206400el3 | \([0, -1, 0, -796033, 9003937]\) | \(54477543627364/31494140625\) | \(32250000000000000000\) | \([2]\) | \(3538944\) | \(2.4328\) | |
| 206400.cp4 | 206400el4 | \([0, -1, 0, -288033, -292464063]\) | \(-2580786074884/34615360125\) | \(-35446128768000000000\) | \([2]\) | \(3538944\) | \(2.4328\) |
Rank
sage: E.rank()
The elliptic curves in class 206400el have rank \(0\).
Complex multiplication
The elliptic curves in class 206400el do not have complex multiplication.Modular form 206400.2.a.el
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.
