Show commands:
SageMath
E = EllipticCurve("gz1")
E.isogeny_class()
Elliptic curves in class 288990.gz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
288990.gz1 | 288990gz2 | \([1, -1, 1, -823907, -284871869]\) | \(651038076963/7220000\) | \(685943908769340000\) | \([2]\) | \(9031680\) | \(2.2368\) | |
288990.gz2 | 288990gz1 | \([1, -1, 1, -93827, 3947779]\) | \(961504803/486400\) | \(46210958064460800\) | \([2]\) | \(4515840\) | \(1.8902\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 288990.gz have rank \(0\).
Complex multiplication
The elliptic curves in class 288990.gz do not have complex multiplication.Modular form 288990.2.a.gz
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.