Properties

Label 270480q
Number of curves $2$
Conductor $270480$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 270480q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270480.q2 270480q1 \([0, -1, 0, -17857576, -1994170109840]\) \(-1306902141891515161/3564268498800000000\) \(-1717586430424355635200000000\) \([2]\) \(149299200\) \(3.9048\) \(\Gamma_0(N)\)-optimal
270480.q1 270480q2 \([0, -1, 0, -2486893096, -47136040329104]\) \(3529773792266261468365081/50841342773437500000\) \(24499950124860000000000000000\) \([2]\) \(298598400\) \(4.2514\)  

Rank

sage: E.rank()
 

The elliptic curves in class 270480q have rank \(0\).

Complex multiplication

The elliptic curves in class 270480q do not have complex multiplication.

Modular form 270480.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - 2 q^{11} + 2 q^{13} + q^{15} + 8 q^{19} + O(q^{20})\) 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.