Properties

Label 310464.f
Number of curves $2$
Conductor $310464$
CM no
Rank $0$
Graph

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

Elliptic curves in class 310464.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
310464.f1 310464f2 \([0, 0, 0, -1169532, 417115440]\) \(4662947952/717409\) \(27218631912869117952\) \([2]\) \(8847360\) \(2.4527\)  
310464.f2 310464f1 \([0, 0, 0, 127008, 35932680]\) \(95551488/290521\) \(-688901324241005568\) \([2]\) \(4423680\) \(2.1061\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 310464.f have rank \(0\).

Complex multiplication

The elliptic curves in class 310464.f do not have complex multiplication.

Modular form 310464.2.a.f

sage: E.q_eigenform(10)
 
\(q - 4 q^{5} - q^{11} + 2 q^{13} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.