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Properties

Label 238050.dg
Number of curves $2$
Conductor $238050$
CM no
Rank $1$
Graph

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

Elliptic curves in class 238050.dg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
238050.dg1 238050dg2 \([1, -1, 0, -28866042, -59659133634]\) \(1577505447721/838350\) \(1413643625296192968750\) \([2]\) \(29196288\) \(3.0081\)  
238050.dg2 238050dg1 \([1, -1, 0, -1490292, -1266658884]\) \(-217081801/285660\) \(-481685976026850937500\) \([2]\) \(14598144\) \(2.6615\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 238050.dg have rank \(1\).

Complex multiplication

The elliptic curves in class 238050.dg do not have complex multiplication.

Modular form 238050.2.a.dg

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 4 q^{7} - q^{8} + 2 q^{11} - 4 q^{13} - 4 q^{14} + q^{16} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.