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Properties

Label 3042.h
Number of curves $2$
Conductor $3042$
CM no
Rank $0$
Graph

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

Elliptic curves in class 3042.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3042.h1 3042e1 \([1, -1, 0, -558, -8748]\) \(-156116857/186624\) \(-22992263424\) \([]\) \(3072\) \(0.68203\) \(\Gamma_0(N)\)-optimal
3042.h2 3042e2 \([1, -1, 0, 4707, 164997]\) \(93603087383/150994944\) \(-18602728095744\) \([]\) \(9216\) \(1.2313\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3042.h have rank \(0\).

Complex multiplication

The elliptic curves in class 3042.h do not have complex multiplication.

Modular form 3042.2.a.h

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.