Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 51520.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51520.y1 | 51520a2 | \([0, 0, 0, -748, 2928]\) | \(1412467848/704375\) | \(23080960000\) | \([2]\) | \(26624\) | \(0.68140\) | |
| 51520.y2 | 51520a1 | \([0, 0, 0, 172, 352]\) | \(137388096/92575\) | \(-379187200\) | \([2]\) | \(13312\) | \(0.33483\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 51520.y have rank \(1\).
Complex multiplication
The elliptic curves in class 51520.y do not have complex multiplication.Modular form 51520.2.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 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.
