Properties

 Label 9702.cc Number of curves $2$ Conductor $9702$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("cc1")

sage: E.isogeny_class()

Elliptic curves in class 9702.cc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.cc1 9702bk1 $$[1, -1, 1, -1259, -6149]$$ $$69426531/34496$$ $$109577337408$$ $$$$ $$9216$$ $$0.81129$$ $$\Gamma_0(N)$$-optimal
9702.cc2 9702bk2 $$[1, -1, 1, 4621, -50837]$$ $$3436115229/2324168$$ $$-7382773107864$$ $$$$ $$18432$$ $$1.1579$$

Rank

sage: E.rank()

The elliptic curves in class 9702.cc have rank $$0$$.

Complex multiplication

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

Modular form9702.2.a.cc

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 2 q^{5} + q^{8} + 2 q^{10} + q^{11} + 4 q^{13} + q^{16} + 2 q^{17} + 6 q^{19} + O(q^{20})$$ 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. 