Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 17424.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17424.y1 | 17424e2 | \([0, 0, 0, -9075, -311454]\) | \(1687500/121\) | \(5926594341888\) | \([2]\) | \(30720\) | \(1.1977\) | |
17424.y2 | 17424e1 | \([0, 0, 0, -1815, 23958]\) | \(54000/11\) | \(134695325952\) | \([2]\) | \(15360\) | \(0.85113\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17424.y have rank \(0\).
Complex multiplication
The elliptic curves in class 17424.y do not have complex multiplication.Modular form 17424.2.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.