Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 333200.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
333200.v1 | 333200v2 | \([0, 1, 0, -549208, 18621588]\) | \(2433138625/1387778\) | \(10449324411008000000\) | \([2]\) | \(5308416\) | \(2.3392\) | |
333200.v2 | 333200v1 | \([0, 1, 0, -353208, -80554412]\) | \(647214625/3332\) | \(25088413952000000\) | \([2]\) | \(2654208\) | \(1.9926\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 333200.v have rank \(1\).
Complex multiplication
The elliptic curves in class 333200.v do not have complex multiplication.Modular form 333200.2.a.v
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.