Properties

Label 235200.vc
Number of curves $4$
Conductor $235200$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("vc1")
 
E.isogeny_class()
 

Elliptic curves in class 235200.vc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.vc1 235200vc4 \([0, 1, 0, -69189633, -221541127137]\) \(608119035935048/826875\) \(49807880640000000000\) \([2]\) \(14155776\) \(3.0538\)  
235200.vc2 235200vc3 \([0, 1, 0, -10977633, 9348832863]\) \(2428799546888/778248135\) \(46878778795322880000000\) \([2]\) \(14155776\) \(3.0538\)  
235200.vc3 235200vc2 \([0, 1, 0, -4362633, -3398272137]\) \(1219555693504/43758225\) \(329479130433600000000\) \([2, 2]\) \(7077888\) \(2.7072\)  
235200.vc4 235200vc1 \([0, 1, 0, 102492, -187847262]\) \(1012048064/130203045\) \(-15318258041205000000\) \([2]\) \(3538944\) \(2.3606\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 235200.vc have rank \(1\).

Complex multiplication

The elliptic curves in class 235200.vc do not have complex multiplication.

Modular form 235200.2.a.vc

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.