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Properties

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

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 277350p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277350.p1 277350p1 \([1, 1, 0, -7143034650, 231776551714500]\) \(408076159454905367161/1190206406250000\) \(117558231205497385253906250000\) \([2]\) \(468357120\) \(4.4485\) \(\Gamma_0(N)\)-optimal
277350.p2 277350p2 \([1, 1, 0, -4253972150, 420989922027000]\) \(-86193969101536367161/725294740213012500\) \(-71638302662759243851173632812500\) \([2]\) \(936714240\) \(4.7951\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 277350.2.a.p

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.