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Properties

Label 7098.m
Number of curves $2$
Conductor $7098$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 7098.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7098.m1 7098n2 \([1, 0, 1, -1706566, -836589544]\) \(673822943613625/19421724672\) \(15842897469754048512\) \([]\) \(235872\) \(2.4621\)  
7098.m2 7098n1 \([1, 0, 1, -223591, 40263914]\) \(1515434103625/17635968\) \(14386200892172928\) \([3]\) \(78624\) \(1.9128\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7098.m have rank \(1\).

Complex multiplication

The elliptic curves in class 7098.m do not have complex multiplication.

Modular form 7098.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + q^{7} - q^{8} + q^{9} - 3 q^{11} + q^{12} - q^{14} + q^{16} - 3 q^{17} - q^{18} + 5 q^{19} + O(q^{20})\) 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.