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Properties

Label 74562t
Number of curves $2$
Conductor $74562$
CM no
Rank $1$
Graph

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

Elliptic curves in class 74562t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
74562.w2 74562t1 \([1, 1, 1, 45945, 8487933]\) \(444369620591/1540767744\) \(-37190387733774336\) \([]\) \(827904\) \(1.8626\) \(\Gamma_0(N)\)-optimal
74562.w1 74562t2 \([1, 1, 1, -17311395, -27733882107]\) \(-23769846831649063249/3261823333284\) \(-78732485772952546596\) \([]\) \(5795328\) \(2.8355\)  

Rank

sage: E.rank()
 

The elliptic curves in class 74562t have rank \(1\).

Complex multiplication

The elliptic curves in class 74562t do not have complex multiplication.

Modular form 74562.2.a.t

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