↑

Properties

Label 79350l
Number of curves $2$
Conductor $79350$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 79350l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
79350.u2 79350l1 \([1, 1, 0, 18125, 182125]\) \(3463512697/2073600\) \(-394210800000000\) \([2]\) \(368640\) \(1.4900\) \(\Gamma_0(N)\)-optimal
79350.u1 79350l2 \([1, 1, 0, -73875, 1378125]\) \(234542659463/131220000\) \(24946152187500000\) \([2]\) \(737280\) \(1.8365\)  

Rank

sage: E.rank()
 

The elliptic curves in class 79350l have rank \(0\).

Complex multiplication

The elliptic curves in class 79350l do not have complex multiplication.

Modular form 79350.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + 4 q^{7} - q^{8} + q^{9} - 2 q^{11} - q^{12} - 2 q^{13} - 4 q^{14} + q^{16} - q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.