Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 415794.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
415794.y1 | 415794y1 | \([1, 1, 1, -37570, 2773391]\) | \(39616946929/226368\) | \(33510588121152\) | \([2]\) | \(3548160\) | \(1.4367\) | \(\Gamma_0(N)\)-optimal |
415794.y2 | 415794y2 | \([1, 1, 1, -16410, 5905071]\) | \(-3301293169/100082952\) | \(-14815868773064328\) | \([2]\) | \(7096320\) | \(1.7833\) |
Rank
sage: E.rank()
The elliptic curves in class 415794.y have rank \(1\).
Complex multiplication
The elliptic curves in class 415794.y do not have complex multiplication.Modular form 415794.2.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.