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Properties

Label 270802.r
Number of curves $2$
Conductor $270802$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 270802.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.r1 270802r2 \([1, -1, 1, -694078299, 7038360693203]\) \(62167173500157644301993/7582456\) \(4510221659256376\) \([2]\) \(46448640\) \(3.3378\)  
270802.r2 270802r1 \([1, -1, 1, -43379779, 109983131651]\) \(-15177411906818559273/167619938752\) \(-99704248634281235392\) \([2]\) \(23224320\) \(2.9912\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 270802.r have rank \(0\).

Complex multiplication

The elliptic curves in class 270802.r do not have complex multiplication.

Modular form 270802.2.a.r

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