Properties

Label 250200c
Number of curves $2$
Conductor $250200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 250200c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
250200.c1 250200c1 \([0, 0, 0, -280875, -57294250]\) \(210094874500/3753\) \(43774992000000\) \([2]\) \(1548288\) \(1.7445\) \(\Gamma_0(N)\)-optimal
250200.c2 250200c2 \([0, 0, 0, -271875, -61137250]\) \(-95269531250/14085009\) \(-328575089952000000\) \([2]\) \(3096576\) \(2.0911\)  

Rank

sage: E.rank()
 

The elliptic curves in class 250200c have rank \(0\).

Complex multiplication

The elliptic curves in class 250200c do not have complex multiplication.

Modular form 250200.2.a.c

sage: E.q_eigenform(10)
 
\(q - 4 q^{7} - 4 q^{11} - 6 q^{13} + 2 q^{17} + O(q^{20})\) 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 Cremona 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 Cremona labels.