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Properties

Label 7098x
Number of curves $3$
Conductor $7098$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 7098x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7098.w3 7098x1 \([1, 0, 0, 2278, 398124]\) \(270840023/14329224\) \(-69164427366216\) \([]\) \(36288\) \(1.3353\) \(\Gamma_0(N)\)-optimal
7098.w2 7098x2 \([1, 0, 0, -20537, -10849671]\) \(-198461344537/10417365504\) \(-50282633570996736\) \([]\) \(108864\) \(1.8846\)  
7098.w1 7098x3 \([1, 0, 0, -4403552, -3557170176]\) \(-1956469094246217097/36641439744\) \(-176861231129296896\) \([]\) \(326592\) \(2.4339\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7098.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 3 q^{5} + q^{6} - q^{7} + q^{8} + q^{9} - 3 q^{10} - 3 q^{11} + q^{12} - q^{14} - 3 q^{15} + q^{16} - 3 q^{17} + q^{18} + 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.