Show commands:
SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 266175.dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 266175.dc1 | 266175dc1 | \([1, -1, 0, -685242, -211161209]\) | \(5177717/189\) | \(1298911271150390625\) | \([2]\) | \(4423680\) | \(2.2453\) | \(\Gamma_0(N)\)-optimal |
| 266175.dc2 | 266175dc2 | \([1, -1, 0, 265383, -752066834]\) | \(300763/35721\) | \(-245494230247423828125\) | \([2]\) | \(8847360\) | \(2.5919\) |
Rank
sage: E.rank()
The elliptic curves in class 266175.dc have rank \(1\).
Complex multiplication
The elliptic curves in class 266175.dc do not have complex multiplication.Modular form 266175.2.a.dc
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.
