# Properties

 Label 1862.f Number of curves $2$ Conductor $1862$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("f1")

E.isogeny_class()

## Elliptic curves in class 1862.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1862.f1 1862f2 $$[1, 0, 0, -3431, 85343]$$ $$-37966934881/4952198$$ $$-582621142502$$ $$[]$$ $$3300$$ $$0.99074$$
1862.f2 1862f1 $$[1, 0, 0, -1, -407]$$ $$-1/608$$ $$-71530592$$ $$[]$$ $$660$$ $$0.18602$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1862.f have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1862.f do not have complex multiplication.

## Modular form1862.2.a.f

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + 4 q^{5} + q^{6} + q^{8} - 2 q^{9} + 4 q^{10} + 2 q^{11} + q^{12} + q^{13} + 4 q^{15} + q^{16} - 3 q^{17} - 2 q^{18} + q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 