Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 28880g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28880.r4 | 28880g1 | \([0, 0, 0, -722, 144039]\) | \(-55296/11875\) | \(-8938717390000\) | \([2]\) | \(46080\) | \(1.1644\) | \(\Gamma_0(N)\)-optimal |
| 28880.r3 | 28880g2 | \([0, 0, 0, -45847, 3745014]\) | \(884901456/9025\) | \(108694803462400\) | \([2, 2]\) | \(92160\) | \(1.5110\) | |
| 28880.r2 | 28880g3 | \([0, 0, 0, -81947, -2976806]\) | \(1263284964/651605\) | \(31391059239941120\) | \([2]\) | \(184320\) | \(1.8575\) | |
| 28880.r1 | 28880g4 | \([0, 0, 0, -731747, 240929234]\) | \(899466517764/95\) | \(4576623303680\) | \([4]\) | \(184320\) | \(1.8575\) |
Rank
sage: E.rank()
The elliptic curves in class 28880g have rank \(1\).
Complex multiplication
The elliptic curves in class 28880g do not have complex multiplication.Modular form 28880.2.a.g
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.
