Properties

 Label 9660.d Number of curves $2$ Conductor $9660$ CM no Rank $1$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 9660.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9660.d1 9660e2 $$[0, 1, 0, -379541, -91405305]$$ $$-23618971583050153984/391556092921875$$ $$-100238359788000000$$ $$[]$$ $$116640$$ $$2.0617$$
9660.d2 9660e1 $$[0, 1, 0, 17899, -600201]$$ $$2477112820760576/2053567248075$$ $$-525713215507200$$ $$$$ $$38880$$ $$1.5124$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 9660.d have rank $$1$$.

Complex multiplication

The elliptic curves in class 9660.d do not have complex multiplication.

Modular form9660.2.a.d

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{7} + q^{9} - 3 q^{11} - 4 q^{13} - q^{15} + 6 q^{17} - q^{19} + O(q^{20})$$ 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels. 