Show commands:
SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 95370.bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95370.bp1 | 95370bj2 | \([1, 0, 1, -41478, 2073406]\) | \(326940373369/112003650\) | \(2703495830126850\) | \([2]\) | \(589824\) | \(1.6631\) | |
95370.bp2 | 95370bj1 | \([1, 0, 1, 7652, 226118]\) | \(2053225511/2098140\) | \(-50643999021660\) | \([2]\) | \(294912\) | \(1.3165\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 95370.bp have rank \(1\).
Complex multiplication
The elliptic curves in class 95370.bp do not have complex multiplication.Modular form 95370.2.a.bp
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.