Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1872.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1872.b1 | 1872g1 | \([0, 0, 0, -5862, 162295]\) | \(1909913257984/129730653\) | \(1513178336592\) | \([2]\) | \(3840\) | \(1.0857\) | \(\Gamma_0(N)\)-optimal |
| 1872.b2 | 1872g2 | \([0, 0, 0, 5073, 698110]\) | \(77366117936/1172914587\) | \(-218894011884288\) | \([2]\) | \(7680\) | \(1.4323\) |
Rank
sage: E.rank()
The elliptic curves in class 1872.b have rank \(0\).
Complex multiplication
The elliptic curves in class 1872.b do not have complex multiplication.Modular form 1872.2.a.b
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.
