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Properties

Label 50430.m
Number of curves $2$
Conductor $50430$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 50430.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50430.m1 50430l2 \([1, 0, 1, -989304, -383479994]\) \(-13410393529/192000\) \(-1533105643991232000\) \([]\) \(1115856\) \(2.2945\)  
50430.m2 50430l1 \([1, 0, 1, 44511, -2622548]\) \(1221431/1080\) \(-8623719247450680\) \([3]\) \(371952\) \(1.7452\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 50430.m have rank \(1\).

Complex multiplication

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

Modular form 50430.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + 2 q^{7} - q^{8} + q^{9} + q^{10} + q^{12} + 5 q^{13} - 2 q^{14} - q^{15} + q^{16} - 3 q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.