Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 99225f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 99225.t2 | 99225f1 | \([0, 0, 1, -22050, -1254094]\) | \(884736/5\) | \(6700478203125\) | \([]\) | \(207360\) | \(1.3030\) | \(\Gamma_0(N)\)-optimal |
| 99225.t1 | 99225f2 | \([0, 0, 1, -132300, 17653781]\) | \(2359296/125\) | \(13568468361328125\) | \([]\) | \(622080\) | \(1.8523\) |
Rank
sage: E.rank()
The elliptic curves in class 99225f have rank \(2\).
Complex multiplication
The elliptic curves in class 99225f do not have complex multiplication.Modular form 99225.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
