↑

Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 79350.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
79350.i1 79350h2 \([1, 1, 0, -62375, 12142125]\) \(-3247061909089/5859375000\) \(-48431396484375000\) \([]\) \(995328\) \(1.8918\)  
79350.i2 79350h1 \([1, 1, 0, 6625, -346875]\) \(3889584671/8640000\) \(-71415000000000\) \([]\) \(331776\) \(1.3424\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 79350.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} + 3 q^{11} - q^{12} + 4 q^{13} + q^{14} + q^{16} + 6 q^{17} - q^{18} - 8 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.