Properties

Label 59976t
Number of curves $2$
Conductor $59976$
CM no
Rank $0$
Graph

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

Elliptic curves in class 59976t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59976.o1 59976t1 \([0, 0, 0, -1911, 13034]\) \(35152/17\) \(373254158592\) \([2]\) \(69120\) \(0.91406\) \(\Gamma_0(N)\)-optimal
59976.o2 59976t2 \([0, 0, 0, 6909, 99470]\) \(415292/289\) \(-25381282784256\) \([2]\) \(138240\) \(1.2606\)  

Rank

sage: E.rank()
 

The elliptic curves in class 59976t have rank \(0\).

Complex multiplication

The elliptic curves in class 59976t do not have complex multiplication.

Modular form 59976.2.a.t

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + 6 q^{11} - 2 q^{13} + q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.