Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 40425y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40425.p3 | 40425y1 | \([1, 1, 1, -7988, 269156]\) | \(30664297/297\) | \(545964890625\) | \([2]\) | \(55296\) | \(1.0719\) | \(\Gamma_0(N)\)-optimal |
| 40425.p2 | 40425y2 | \([1, 1, 1, -14113, -208594]\) | \(169112377/88209\) | \(162151572515625\) | \([2, 2]\) | \(110592\) | \(1.4185\) | |
| 40425.p4 | 40425y3 | \([1, 1, 1, 53262, -1556094]\) | \(9090072503/5845851\) | \(-10746226942171875\) | \([2]\) | \(221184\) | \(1.7650\) | |
| 40425.p1 | 40425y4 | \([1, 1, 1, -179488, -29314594]\) | \(347873904937/395307\) | \(726679269421875\) | \([2]\) | \(221184\) | \(1.7650\) |
Rank
sage: E.rank()
The elliptic curves in class 40425y have rank \(1\).
Complex multiplication
The elliptic curves in class 40425y do not have complex multiplication.Modular form 40425.2.a.y
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.
