Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 74025.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 74025.i1 | 74025bj1 | \([1, -1, 1, -161555, -24952678]\) | \(327510203957/6909\) | \(9837228515625\) | \([2]\) | \(348160\) | \(1.6110\) | \(\Gamma_0(N)\)-optimal |
| 74025.i2 | 74025bj2 | \([1, -1, 1, -155930, -26775178]\) | \(-294477807077/47734281\) | \(-67965411814453125\) | \([2]\) | \(696320\) | \(1.9575\) |
Rank
sage: E.rank()
The elliptic curves in class 74025.i have rank \(0\).
Complex multiplication
The elliptic curves in class 74025.i do not have complex multiplication.Modular form 74025.2.a.i
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.
