Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 134310.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
134310.w1 | 134310bx2 | \([1, 0, 1, -6174, -185858]\) | \(14688124849/123210\) | \(218274030810\) | \([2]\) | \(224000\) | \(1.0013\) | |
134310.w2 | 134310bx1 | \([1, 0, 1, -124, -6778]\) | \(-117649/11100\) | \(-19664327100\) | \([2]\) | \(112000\) | \(0.65475\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 134310.w have rank \(0\).
Complex multiplication
The elliptic curves in class 134310.w do not have complex multiplication.Modular form 134310.2.a.w
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.