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Properties

Label 98826t
Number of curves $2$
Conductor $98826$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 98826t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
98826.p2 98826t1 \([1, 0, 0, -3333198596, 103601868154512]\) \(-4095503324447959733993040498942529/2266747861853082876455402377344\) \(-2266747861853082876455402377344\) \([7]\) \(169645056\) \(4.5281\) \(\Gamma_0(N)\)-optimal
98826.p1 98826t2 \([1, 0, 0, -223463519006, -45977186665875738]\) \(-1234080849062768060834770773940209593569/199037633915785610874310991934937794\) \(-199037633915785610874310991934937794\) \([]\) \(1187515392\) \(5.5011\)  

Rank

sage: E.rank()
 

The elliptic curves in class 98826t have rank \(1\).

Complex multiplication

The elliptic curves in class 98826t do not have complex multiplication.

Modular form 98826.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} + 5 q^{11} + q^{12} + q^{13} + q^{14} - q^{15} + q^{16} - 3 q^{17} + q^{18} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.