Properties

Label 301180.h
Number of curves $2$
Conductor $301180$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 301180.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
301180.h1 301180h2 \([0, -1, 0, -82596, 9141320]\) \(94875856/275\) \(180627139193600\) \([2]\) \(1216512\) \(1.6064\)  
301180.h2 301180h1 \([0, -1, 0, -7301, 15566]\) \(1048576/605\) \(24836231639120\) \([2]\) \(608256\) \(1.2598\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 301180.h have rank \(1\).

Complex multiplication

The elliptic curves in class 301180.h do not have complex multiplication.

Modular form 301180.2.a.h

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