# Properties

 Label 900.e Number of curves $2$ Conductor $900$ CM no Rank $1$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 900.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
900.e1 900d2 $$[0, 0, 0, -10920, 439220]$$ $$-30866268160/3$$ $$-13996800$$ $$[]$$ $$864$$ $$0.80452$$
900.e2 900d1 $$[0, 0, 0, -120, 740]$$ $$-40960/27$$ $$-125971200$$ $$[]$$ $$288$$ $$0.25522$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 900.e have rank $$1$$.

## Complex multiplication

The elliptic curves in class 900.e do not have complex multiplication.

## Modular form900.2.a.e

sage: E.q_eigenform(10)

$$q + q^{7} - 6q^{11} - 5q^{13} - 6q^{17} + 5q^{19} + O(q^{20})$$ ## 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. 