Properties

Label 93600.ev
Number of curves $2$
Conductor $93600$
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 93600.ev

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.ev1 93600ey2 \([0, 0, 0, -2235, 13250]\) \(26463592/13689\) \(638673984000\) \([2]\) \(114688\) \(0.95725\)  
93600.ev2 93600ey1 \([0, 0, 0, -1785, 29000]\) \(107850176/117\) \(682344000\) \([2]\) \(57344\) \(0.61068\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 93600.ev have rank \(0\).

Complex multiplication

The elliptic curves in class 93600.ev do not have complex multiplication.

Modular form 93600.2.a.ev

sage: E.q_eigenform(10)
 
\(q + 4q^{7} + 2q^{11} - q^{13} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.