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Properties

Label 433200dg
Number of curves $2$
Conductor $433200$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dg1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 433200dg have rank \(0\).

Complex multiplication

The elliptic curves in class 433200dg do not have complex multiplication.

Modular form 433200.2.a.dg

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{9} + 4 q^{11} + 4 q^{13} + 6 q^{17} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 433200dg

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
433200.dg2 433200dg1 \([0, -1, 0, 23750792, 27677356912]\) \(3936827539/3158028\) \(-1188577675861344000000000\) \([2]\) \(58060800\) \(3.3074\) \(\Gamma_0(N)\)-optimal*
433200.dg1 433200dg2 \([0, -1, 0, -113429208, 240580716912]\) \(428831641421/181752822\) \(68405773081809456000000000\) \([2]\) \(116121600\) \(3.6540\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 433200dg1.