Properties

Label 39600dv
Number of curves $4$
Conductor $39600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("dv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 39600dv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39600.ea4 39600dv1 \([0, 0, 0, 49200, -15433625]\) \(72268906496/606436875\) \(-110523120468750000\) \([2]\) \(221184\) \(1.9517\) \(\Gamma_0(N)\)-optimal
39600.ea3 39600dv2 \([0, 0, 0, -710175, -212111750]\) \(13584145739344/1195803675\) \(3486963516300000000\) \([2]\) \(442368\) \(2.2983\)  
39600.ea2 39600dv3 \([0, 0, 0, -3514800, -2538300125]\) \(-26348629355659264/24169921875\) \(-4404968261718750000\) \([2]\) \(663552\) \(2.5010\)  
39600.ea1 39600dv4 \([0, 0, 0, -56249175, -162376190750]\) \(6749703004355978704/5671875\) \(16539187500000000\) \([2]\) \(1327104\) \(2.8476\)  

Rank

sage: E.rank()
 

The elliptic curves in class 39600dv have rank \(0\).

Complex multiplication

The elliptic curves in class 39600dv do not have complex multiplication.

Modular form 39600.2.a.dv

sage: E.q_eigenform(10)
 
\(q + 2q^{7} + q^{11} - 2q^{13} - 2q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.