Properties

Label 190575.ev
Number of curves $2$
Conductor $190575$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ev1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 190575.ev

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
190575.ev1 190575er2 [0, 0, 1, -729366825, -143336942153969] [] 691200000  
190575.ev2 190575er1 [0, 0, 1, -243400575, 1711662797281] [] 138240000 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 190575.ev have rank \(0\).

Complex multiplication

The elliptic curves in class 190575.ev do not have complex multiplication.

Modular form 190575.2.a.ev

sage: E.q_eigenform(10)
 
\( q + 2q^{2} + 2q^{4} + q^{7} - 6q^{13} + 2q^{14} - 4q^{16} + 7q^{17} + 5q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.