Properties

Label 32340.v
Number of curves $2$
Conductor $32340$
CM no
Rank $0$
Graph

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

Elliptic curves in class 32340.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.v1 32340bb2 \([0, 1, 0, -4832355516, 128975649586020]\) \(414354576760345737269208016/1182266314178222109375\) \(35607667096768935154140000000\) \([2]\) \(41932800\) \(4.3500\)  
32340.v2 32340bb1 \([0, 1, 0, -181183641, 3643311773520]\) \(-349439858058052607328256/2844147488104248046875\) \(-5353777725247626855468750000\) \([2]\) \(20966400\) \(4.0034\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 32340.v have rank \(0\).

Complex multiplication

The elliptic curves in class 32340.v do not have complex multiplication.

Modular form 32340.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} - q^{11} - 4q^{13} - q^{15} - 2q^{17} - 2q^{19} + O(q^{20})\)  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.