Show commands:
SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 173264.cv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
173264.cv1 | 173264bw1 | \([0, -1, 0, -46664, 3895088]\) | \(23320116793/2873\) | \(1384470843392\) | \([2]\) | \(552960\) | \(1.3531\) | \(\Gamma_0(N)\)-optimal |
173264.cv2 | 173264bw2 | \([0, -1, 0, -42744, 4572464]\) | \(-17923019113/8254129\) | \(-3977584733065216\) | \([2]\) | \(1105920\) | \(1.6997\) |
Rank
sage: E.rank()
The elliptic curves in class 173264.cv have rank \(0\).
Complex multiplication
The elliptic curves in class 173264.cv do not have complex multiplication.Modular form 173264.2.a.cv
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.