Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1530.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1530.g1 | 1530g2 | \([1, -1, 0, -59769, 5820525]\) | \(-32391289681150609/1228250000000\) | \(-895394250000000\) | \([3]\) | \(7560\) | \(1.6391\) | |
1530.g2 | 1530g1 | \([1, -1, 0, 3591, 24813]\) | \(7023836099951/4456448000\) | \(-3248750592000\) | \([]\) | \(2520\) | \(1.0898\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1530.g have rank \(0\).
Complex multiplication
The elliptic curves in class 1530.g do not have complex multiplication.Modular form 1530.2.a.g
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.