Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 225400.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 225400.l1 | 225400bp2 | \([0, 1, 0, -22932408, -42275537312]\) | \(2065714832668/66125\) | \(42694116206000000000\) | \([2]\) | \(12386304\) | \(2.8618\) | |
| 225400.l2 | 225400bp1 | \([0, 1, 0, -1494908, -601037312]\) | \(2288890672/359375\) | \(58008310062500000000\) | \([2]\) | \(6193152\) | \(2.5152\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 225400.l have rank \(0\).
Complex multiplication
The elliptic curves in class 225400.l do not have complex multiplication.Modular form 225400.2.a.l
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
