Properties

Label 91728da
Number of curves $2$
Conductor $91728$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("da1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 91728da have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(7\)\(1\)
\(13\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + 5 T^{2}\) 1.5.a
\(11\) \( 1 + 3 T + 11 T^{2}\) 1.11.d
\(17\) \( 1 + 3 T + 17 T^{2}\) 1.17.d
\(19\) \( 1 + 5 T + 19 T^{2}\) 1.19.f
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 - 9 T + 29 T^{2}\) 1.29.aj
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 91728da do not have complex multiplication.

Modular form 91728.2.a.da

Copy content sage:E.q_eigenform(10)
 
\(q + 4 q^{5} + 4 q^{11} + q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.

Elliptic curves in class 91728da

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91728.gg2 91728da1 \([0, 0, 0, -48363, -2857190]\) \(2803221/832\) \(3713038039646208\) \([2]\) \(645120\) \(1.6931\) \(\Gamma_0(N)\)-optimal
91728.gg1 91728da2 \([0, 0, 0, -706923, -228743270]\) \(8754552981/1352\) \(6033686814425088\) \([2]\) \(1290240\) \(2.0397\)