Properties

 Label 1170.d Number of curves $2$ Conductor $1170$ CM no Rank $1$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 1170.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1170.d1 1170f1 $$[1, -1, 0, -7569, 255325]$$ $$65787589563409/10400000$$ $$7581600000$$ $$$$ $$1920$$ $$0.90626$$ $$\Gamma_0(N)$$-optimal
1170.d2 1170f2 $$[1, -1, 0, -6849, 305293]$$ $$-48743122863889/26406250000$$ $$-19250156250000$$ $$$$ $$3840$$ $$1.2528$$

Rank

sage: E.rank()

The elliptic curves in class 1170.d have rank $$1$$.

Complex multiplication

The elliptic curves in class 1170.d do not have complex multiplication.

Modular form1170.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} - 4 q^{7} - q^{8} - q^{10} + 2 q^{11} - q^{13} + 4 q^{14} + q^{16} - 2 q^{17} + 6 q^{19} + O(q^{20})$$ 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. 