Show commands:
SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 57960bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57960.x1 | 57960bg1 | \([0, 0, 0, -783, 2322]\) | \(10536048/5635\) | \(28393908480\) | \([2]\) | \(46080\) | \(0.69705\) | \(\Gamma_0(N)\)-optimal |
57960.x2 | 57960bg2 | \([0, 0, 0, 2997, 18198]\) | \(147704148/92575\) | \(-1865885414400\) | \([2]\) | \(92160\) | \(1.0436\) |
Rank
sage: E.rank()
The elliptic curves in class 57960bg have rank \(1\).
Complex multiplication
The elliptic curves in class 57960bg do not have complex multiplication.Modular form 57960.2.a.bg
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 Cremona 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 Cremona labels.