Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 76050.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76050.v1 | 76050t2 | \([1, -1, 0, -1661217, -823701709]\) | \(-8538302475/26\) | \(-1543848825138750\) | \([]\) | \(1306368\) | \(2.1416\) | |
| 76050.v2 | 76050t1 | \([1, -1, 0, -13467, -1913859]\) | \(-3316275/17576\) | \(-1431607415355000\) | \([]\) | \(435456\) | \(1.5923\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 76050.v have rank \(0\).
Complex multiplication
The elliptic curves in class 76050.v do not have complex multiplication.Modular form 76050.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
