Properties

Label 59248.f
Number of curves $2$
Conductor $59248$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 59248.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59248.f1 59248bc2 \([0, 1, 0, -5125128, 4179245044]\) \(24553362849625/1755162752\) \(1064251712847898738688\) \([2]\) \(2838528\) \(2.7816\)  
59248.f2 59248bc1 \([0, 1, 0, 291832, 285534196]\) \(4533086375/60669952\) \(-36787528826500415488\) \([2]\) \(1419264\) \(2.4351\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 59248.f have rank \(0\).

Complex multiplication

The elliptic curves in class 59248.f do not have complex multiplication.

Modular form 59248.2.a.f

sage: E.q_eigenform(10)
 
\(q - 2q^{3} + q^{7} + q^{9} + 4q^{11} - 6q^{17} - 6q^{19} + O(q^{20})\)  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.