Properties

Label 418950.u
Number of curves $2$
Conductor $418950$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 418950.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
418950.u1 418950u2 \([1, -1, 0, -22033692, -39718804784]\) \(882774443450089/2166000000\) \(2902647157593750000000\) \([2]\) \(46448640\) \(2.9965\) \(\Gamma_0(N)\)-optimal*
418950.u2 418950u1 \([1, -1, 0, -865692, -1087204784]\) \(-53540005609/350208000\) \(-469312214112000000000\) \([2]\) \(23224320\) \(2.6499\) \(\Gamma_0(N)\)-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 418950.u1.

Rank

sage: E.rank()
 

The elliptic curves in class 418950.u have rank \(1\).

Complex multiplication

The elliptic curves in class 418950.u do not have complex multiplication.

Modular form 418950.2.a.u

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