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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 327990.bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
327990.bp1 | 327990bp2 | \([1, 0, 0, -716970, -233727228]\) | \(68523370149961/243360\) | \(144756203398560\) | \([2]\) | \(3745280\) | \(1.9355\) | |
327990.bp2 | 327990bp1 | \([1, 0, 0, -44170, -3764188]\) | \(-16022066761/998400\) | \(-593871603686400\) | \([2]\) | \(1872640\) | \(1.5889\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 327990.bp have rank \(0\).
Complex multiplication
The elliptic curves in class 327990.bp do not have complex multiplication.Modular form 327990.2.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.