Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 262626.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
262626.p1 | 262626p2 | \([1, 0, 1, -403407, -98652734]\) | \(1504154129818033/5519808\) | \(26643058932672\) | \([2]\) | \(2073600\) | \(1.7926\) | |
262626.p2 | 262626p1 | \([1, 0, 1, -24847, -1589950]\) | \(-351447414193/22278144\) | \(-107532345962496\) | \([2]\) | \(1036800\) | \(1.4460\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 262626.p have rank \(1\).
Complex multiplication
The elliptic curves in class 262626.p do not have complex multiplication.Modular form 262626.2.a.p
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.