Properties

Label 9702.m
Number of curves $4$
Conductor $9702$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 9702.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.m1 9702i4 \([1, -1, 0, -451887, 117033965]\) \(4406910829875/7744\) \(17932666707648\) \([2]\) \(69120\) \(1.8023\)  
9702.m2 9702i3 \([1, -1, 0, -28527, 1795373]\) \(1108717875/45056\) \(104335515389952\) \([2]\) \(34560\) \(1.4557\)  
9702.m3 9702i2 \([1, -1, 0, -7212, 60724]\) \(13060888875/7086244\) \(22509617049612\) \([2]\) \(23040\) \(1.2530\)  
9702.m4 9702i1 \([1, -1, 0, -4272, -105680]\) \(2714704875/21296\) \(67647233808\) \([2]\) \(11520\) \(0.90644\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9702.m have rank \(1\).

Complex multiplication

The elliptic curves in class 9702.m do not have complex multiplication.

Modular form 9702.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{8} + q^{11} - 2 q^{13} + q^{16} - 6 q^{17} - 2 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.