Properties

Label 418950.nh
Number of curves $2$
Conductor $418950$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("nh1")
 
E.isogeny_class()
 

Elliptic curves in class 418950.nh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
418950.nh1 418950nh2 \([1, -1, 1, -330980, -72053103]\) \(2992209121/54150\) \(72566178939843750\) \([2]\) \(6635520\) \(2.0306\) \(\Gamma_0(N)\)-optimal*
418950.nh2 418950nh1 \([1, -1, 1, -230, -3257103]\) \(-1/3420\) \(-4583127090937500\) \([2]\) \(3317760\) \(1.6840\) \(\Gamma_0(N)\)-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.nh1.

Rank

sage: E.rank()
 

The elliptic curves in class 418950.nh have rank \(0\).

Complex multiplication

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

Modular form 418950.2.a.nh

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