# Properties

 Label 2450.x Number of curves $2$ Conductor $2450$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("x1")

sage: E.isogeny_class()

## Elliptic curves in class 2450.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2450.x1 2450bf2 $$[1, 1, 1, -55763, 7098531]$$ $$-417267265/235298$$ $$-10813505625781250$$ $$[]$$ $$17280$$ $$1.7798$$
2450.x2 2450bf1 $$[1, 1, 1, 5487, -128969]$$ $$397535/392$$ $$-18015003125000$$ $$[]$$ $$5760$$ $$1.2305$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2450.x have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2450.x do not have complex multiplication.

## Modular form2450.2.a.x

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} - 2 q^{9} + 3 q^{11} - q^{12} - 2 q^{13} + q^{16} - 3 q^{17} - 2 q^{18} + 7 q^{19} + O(q^{20})$$ ## 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. 