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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 19266.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19266.i1 | 19266g3 | \([1, 0, 1, -72336, -7494134]\) | \(8671983378625/82308\) | \(397284995172\) | \([2]\) | \(77760\) | \(1.3880\) | |
| 19266.i2 | 19266g4 | \([1, 0, 1, -70646, -7860526]\) | \(-8078253774625/846825858\) | \(-4087466672827122\) | \([2]\) | \(155520\) | \(1.7346\) | |
| 19266.i3 | 19266g1 | \([1, 0, 1, -1356, 1354]\) | \(57066625/32832\) | \(158473793088\) | \([2]\) | \(25920\) | \(0.83867\) | \(\Gamma_0(N)\)-optimal |
| 19266.i4 | 19266g2 | \([1, 0, 1, 5404, 12170]\) | \(3616805375/2105352\) | \(-10162131981768\) | \([2]\) | \(51840\) | \(1.1852\) |
Rank
sage: E.rank()
The elliptic curves in class 19266.i have rank \(0\).
Complex multiplication
The elliptic curves in class 19266.i do not have complex multiplication.Modular form 19266.2.a.i
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
