Properties

 Label 1710.l Number of curves $4$ Conductor $1710$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

Elliptic curves in class 1710.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1710.l1 1710n4 $$[1, -1, 1, -8708, 314867]$$ $$100162392144121/23457780$$ $$17100721620$$ $$$$ $$4096$$ $$0.95399$$
1710.l2 1710n3 $$[1, -1, 1, -4028, -94669]$$ $$9912050027641/311647500$$ $$227191027500$$ $$$$ $$4096$$ $$0.95399$$
1710.l3 1710n2 $$[1, -1, 1, -608, 3827]$$ $$34043726521/11696400$$ $$8526675600$$ $$[2, 2]$$ $$2048$$ $$0.60742$$
1710.l4 1710n1 $$[1, -1, 1, 112, 371]$$ $$214921799/218880$$ $$-159563520$$ $$$$ $$1024$$ $$0.26085$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 1710.l have rank $$1$$.

Complex multiplication

The elliptic curves in class 1710.l do not have complex multiplication.

Modular form1710.2.a.l

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels. 