Properties

Label 277350dh
Number of curves $2$
Conductor $277350$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dh1")
 
E.isogeny_class()
 

Elliptic curves in class 277350dh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277350.dh2 277350dh1 \([1, 0, 0, 7348812, -17130673008]\) \(444369620591/1540767744\) \(-152183629437698304000000\) \([]\) \(43464960\) \(3.1313\) \(\Gamma_0(N)\)-optimal
277350.dh1 277350dh2 \([1, 0, 0, -2768924688, 56087299131492]\) \(-23769846831649063249/3261823333284\) \(-322174523302929522233062500\) \([]\) \(304254720\) \(4.1042\)  

Rank

sage: E.rank()
 

The elliptic curves in class 277350dh have rank \(0\).

Complex multiplication

The elliptic curves in class 277350dh do not have complex multiplication.

Modular form 277350.2.a.dh

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