Properties

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

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

Elliptic curves in class 9702.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.d1 9702g2 $$[1, -1, 0, -11239188, -14499945776]$$ $$144106117295241933/247808$$ $$269998559373312$$ $$$$ $$275968$$ $$2.4580$$
9702.d2 9702g1 $$[1, -1, 0, -702228, -226579760]$$ $$-35148950502093/46137344$$ $$-50268822690594816$$ $$$$ $$137984$$ $$2.1115$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form9702.2.a.d

sage: E.q_eigenform(10)

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