Show commands:
SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 457776.dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 457776.dg1 | 457776dg1 | \([0, 0, 0, -8240835, 9105174466]\) | \(858729462625/38148\) | \(2749494014085316608\) | \([2]\) | \(14155776\) | \(2.6155\) | \(\Gamma_0(N)\)-optimal |
| 457776.dg2 | 457776dg2 | \([0, 0, 0, -7824675, 10065921442]\) | \(-735091890625/181908738\) | \(-13110962206165832245248\) | \([2]\) | \(28311552\) | \(2.9621\) |
Rank
sage: E.rank()
The elliptic curves in class 457776.dg have rank \(1\).
Complex multiplication
The elliptic curves in class 457776.dg do not have complex multiplication.Modular form 457776.2.a.dg
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.
