# Properties

 Label 4900.f Number of curves $2$ Conductor $4900$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 4900.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4900.f1 4900m2 $$[0, 1, 0, -4818, 127273]$$ $$-262885120/343$$ $$-16141442800$$ $$[]$$ $$5184$$ $$0.86578$$
4900.f2 4900m1 $$[0, 1, 0, 82, 853]$$ $$1280/7$$ $$-329417200$$ $$[]$$ $$1728$$ $$0.31647$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4900.f have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4900.f do not have complex multiplication.

## Modular form4900.2.a.f

sage: E.q_eigenform(10)

$$q - 2 q^{3} + q^{9} + 3 q^{11} - 4 q^{13} - 2 q^{19} + O(q^{20})$$ ## 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. 