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Properties

Label 50430p
Number of curves $2$
Conductor $50430$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 50430p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50430.q2 50430p1 \([1, 1, 1, -1506211, -534719311]\) \(1154320649/291600\) \(95464572069279027600\) \([2]\) \(1889280\) \(2.5436\) \(\Gamma_0(N)\)-optimal
50430.q1 50430p2 \([1, 1, 1, -8398311, 8923998729]\) \(200098975049/10628820\) \(3479683651925220556020\) \([2]\) \(3778560\) \(2.8902\)  

Rank

sage: E.rank()
 

The elliptic curves in class 50430p have rank \(0\).

Complex multiplication

The elliptic curves in class 50430p do not have complex multiplication.

Modular form 50430.2.a.p

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + q^{8} + q^{9} - q^{10} + 2 q^{11} - q^{12} + 2 q^{13} + q^{15} + q^{16} + 6 q^{17} + q^{18} + 2 q^{19} + O(q^{20})\) 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 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.