Show commands:
SageMath
E = EllipticCurve("iq1")
E.isogeny_class()
Elliptic curves in class 270480iq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270480.iq4 | 270480iq1 | \([0, 1, 0, -193860, -210351492]\) | \(-26752376766544/618796614375\) | \(-18637005538458720000\) | \([2]\) | \(4718592\) | \(2.3784\) | \(\Gamma_0(N)\)-optimal |
| 270480.iq3 | 270480iq2 | \([0, 1, 0, -6623640, -6534683100]\) | \(266763091319403556/1355769140625\) | \(163333000832400000000\) | \([2, 2]\) | \(9437184\) | \(2.7250\) | |
| 270480.iq2 | 270480iq3 | \([0, 1, 0, -10275120, 1467900468]\) | \(497927680189263938/284271240234375\) | \(68493777187500000000000\) | \([2]\) | \(18874368\) | \(3.0715\) | |
| 270480.iq1 | 270480iq4 | \([0, 1, 0, -105848640, -419191613100]\) | \(544328872410114151778/14166950625\) | \(3413458071717120000\) | \([2]\) | \(18874368\) | \(3.0715\) |
Rank
sage: E.rank()
The elliptic curves in class 270480iq have rank \(1\).
Complex multiplication
The elliptic curves in class 270480iq do not have complex multiplication.Modular form 270480.2.a.iq
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.
