Properties

Label 94640.f
Number of curves $2$
Conductor $94640$
CM no
Rank $1$
Graph

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

Elliptic curves in class 94640.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
94640.f1 94640e2 \([0, 1, 0, -142016, -1215980]\) \(32044133522/18484375\) \(182723681504000000\) \([2]\) \(1032192\) \(2.0018\)  
94640.f2 94640e1 \([0, 1, 0, -94696, 11144004]\) \(19000416964/79625\) \(393558698624000\) \([2]\) \(516096\) \(1.6552\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 94640.f have rank \(1\).

Complex multiplication

The elliptic curves in class 94640.f do not have complex multiplication.

Modular form 94640.2.a.f

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{5} - q^{7} + q^{9} - 4 q^{11} + 2 q^{15} + 4 q^{17} + 6 q^{19} + O(q^{20})\) 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.