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Properties

Label 300042h
Number of curves $2$
Conductor $300042$
CM no
Rank $0$
Graph

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

Elliptic curves in class 300042h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
300042.h2 300042h1 \([1, -1, 0, -105363, -13014243]\) \(177444640175483953/1913455446264\) \(1394909020326456\) \([]\) \(3237120\) \(1.7214\) \(\Gamma_0(N)\)-optimal
300042.h1 300042h2 \([1, -1, 0, -783333, 259831503]\) \(72918170522696196433/2250945132306174\) \(1640939001451200846\) \([3]\) \(9711360\) \(2.2707\)  

Rank

sage: E.rank()
 

The elliptic curves in class 300042h have rank \(0\).

Complex multiplication

The elliptic curves in class 300042h do not have complex multiplication.

Modular form 300042.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 3 q^{5} + 2 q^{7} - q^{8} - 3 q^{10} + 6 q^{11} - 4 q^{13} - 2 q^{14} + q^{16} - 6 q^{17} - 7 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.