Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 42483.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42483.u1 | 42483k2 | \([1, 1, 0, -31651, 2150380]\) | \(423564751/867\) | \(7178054406789\) | \([2]\) | \(147456\) | \(1.3532\) | |
42483.u2 | 42483k1 | \([1, 1, 0, -1306, 56575]\) | \(-29791/153\) | \(-1266715483551\) | \([2]\) | \(73728\) | \(1.0066\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 42483.u have rank \(0\).
Complex multiplication
The elliptic curves in class 42483.u do not have complex multiplication.Modular form 42483.2.a.u
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.