Properties

Label 119952.fv
Number of curves $2$
Conductor $119952$
CM no
Rank $0$
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Show commands: SageMath
sage: E = EllipticCurve("fv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 119952.fv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.fv1 119952dd2 \([0, 0, 0, -7531839, -7530582150]\) \(79708988544624/4802079233\) \(2846746657491138614016\) \([2]\) \(6082560\) \(2.8692\)  
119952.fv2 119952dd1 \([0, 0, 0, -7419384, -7778545425]\) \(1219067475001344/4857223\) \(179964795834136656\) \([2]\) \(3041280\) \(2.5227\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 119952.fv have rank \(0\).

Complex multiplication

The elliptic curves in class 119952.fv do not have complex multiplication.

Modular form 119952.2.a.fv

sage: E.q_eigenform(10)
 
\(q + 2q^{5} + 2q^{11} + 6q^{13} + q^{17} - 2q^{19} + O(q^{20})\)  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.