Show commands:
SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 164730dg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
164730.j2 | 164730dg1 | \([1, 1, 0, -61418, 6095808]\) | \(-1061520150601/56337660\) | \(-1359854155548540\) | \([2]\) | \(884736\) | \(1.6630\) | \(\Gamma_0(N)\)-optimal |
164730.j1 | 164730dg2 | \([1, 1, 0, -994888, 381537442]\) | \(4511837439092521/11773350\) | \(284180047986150\) | \([2]\) | \(1769472\) | \(2.0095\) |
Rank
sage: E.rank()
The elliptic curves in class 164730dg have rank \(2\).
Complex multiplication
The elliptic curves in class 164730dg do not have complex multiplication.Modular form 164730.2.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 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.