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Properties

Label 63870p
Number of curves $2$
Conductor $63870$
CM no
Rank $1$
Graph

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

Elliptic curves in class 63870p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63870.o2 63870p1 \([1, 0, 0, -35874060, 82698195600]\) \(5105817686570071165887579841/97645976616960000000\) \(97645976616960000000\) \([7]\) \(4346496\) \(2.9589\) \(\Gamma_0(N)\)-optimal
63870.o1 63870p2 \([1, 0, 0, -1345660860, -18997123438560]\) \(269482504024993568727413630831041/47581800502396103180402160\) \(47581800502396103180402160\) \([]\) \(30425472\) \(3.9319\)  

Rank

sage: E.rank()
 

The elliptic curves in class 63870p have rank \(1\).

Complex multiplication

The elliptic curves in class 63870p do not have complex multiplication.

Modular form 63870.2.a.p

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} + q^{14} + q^{15} + q^{16} - 3 q^{17} + q^{18} + 6 q^{19} + O(q^{20})\) 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 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.