Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 17424.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17424.i1 | 17424bz3 | \([0, 0, 0, -6133611, 5846856730]\) | \(4824238966273/66\) | \(349130284867584\) | \([4]\) | \(368640\) | \(2.3464\) | |
17424.i2 | 17424bz2 | \([0, 0, 0, -383691, 91186810]\) | \(1180932193/4356\) | \(23042598801260544\) | \([2, 2]\) | \(184320\) | \(1.9999\) | |
17424.i3 | 17424bz4 | \([0, 0, 0, -209451, 174368986]\) | \(-192100033/2371842\) | \(-12546695047286366208\) | \([2]\) | \(368640\) | \(2.3464\) | |
17424.i4 | 17424bz1 | \([0, 0, 0, -35211, -45254]\) | \(912673/528\) | \(2793042278940672\) | \([2]\) | \(92160\) | \(1.6533\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17424.i have rank \(0\).
Complex multiplication
The elliptic curves in class 17424.i do not have complex multiplication.Modular form 17424.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.