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Properties

Label 304434.h
Number of curves $2$
Conductor $304434$
CM no
Rank $0$
Graph

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

Elliptic curves in class 304434.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
304434.h1 304434h2 \([1, -1, 0, -30014660034, 2001475345718916]\) \(-4102007684809181687432274264918049/3936639679171948631439024\) \(-2869810326116350552319048496\) \([]\) \(559161344\) \(4.5635\)  
304434.h2 304434h1 \([1, -1, 0, 80445006, -61258147884]\) \(78975693098270145722349791/47925805879636550221824\) \(-34937912486255045111709696\) \([]\) \(79880192\) \(3.5905\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 304434.h have rank \(0\).

Complex multiplication

The elliptic curves in class 304434.h do not have complex multiplication.

Modular form 304434.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - q^{10} - 5 q^{11} + q^{13} - q^{14} + q^{16} - 4 q^{17} + 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.