Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 7938.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7938.l1 | 7938h2 | \([1, -1, 0, -4713, 154853]\) | \(-185193/56\) | \(-3501316123704\) | \([]\) | \(20736\) | \(1.1210\) | |
7938.l2 | 7938h1 | \([1, -1, 0, 432, -1898]\) | \(934407/686\) | \(-6537284334\) | \([]\) | \(6912\) | \(0.57169\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7938.l have rank \(0\).
Complex multiplication
The elliptic curves in class 7938.l do not have complex multiplication.Modular form 7938.2.a.l
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.