Properties

Label 8880.v
Number of curves $2$
Conductor $8880$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 8880.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8880.v1 8880t2 \([0, 1, 0, -338336, 75614964]\) \(1045706191321645729/323352324000\) \(1324451119104000\) \([2]\) \(57600\) \(1.8781\)  
8880.v2 8880t1 \([0, 1, 0, -18336, 1502964]\) \(-166456688365729/143856000000\) \(-589234176000000\) \([2]\) \(28800\) \(1.5316\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8880.v have rank \(1\).

Complex multiplication

The elliptic curves in class 8880.v do not have complex multiplication.

Modular form 8880.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} + 2 q^{11} - 2 q^{13} - q^{15} + 6 q^{17} - 6 q^{19} + O(q^{20})\) 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.