# Properties

 Label 1900.a Number of curves $2$ Conductor $1900$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 1900.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1900.a1 1900a1 $$[0, 1, 0, -23033, 1247188]$$ $$5405726654464/407253125$$ $$101813281250000$$ $$$$ $$5760$$ $$1.4331$$ $$\Gamma_0(N)$$-optimal
1900.a2 1900a2 $$[0, 1, 0, 22092, 5579188]$$ $$298091207216/3525390625$$ $$-14101562500000000$$ $$$$ $$11520$$ $$1.7797$$

## Rank

sage: E.rank()

The elliptic curves in class 1900.a have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1900.a do not have complex multiplication.

## Modular form1900.2.a.a

sage: E.q_eigenform(10)

$$q - 2q^{3} - 2q^{7} + q^{9} - 6q^{13} - 2q^{17} - q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 