# Properties

 Label 1950i Number of curves $2$ Conductor $1950$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 1950i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.h2 1950i1 $$[1, 0, 1, 99, -1052]$$ $$6967871/35100$$ $$-548437500$$ $$$$ $$1152$$ $$0.35910$$ $$\Gamma_0(N)$$-optimal
1950.h1 1950i2 $$[1, 0, 1, -1151, -13552]$$ $$10779215329/1232010$$ $$19250156250$$ $$$$ $$2304$$ $$0.70568$$

## Rank

sage: E.rank()

The elliptic curves in class 1950i have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1950i do not have complex multiplication.

## Modular form1950.2.a.i

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - 2q^{7} - q^{8} + q^{9} + 4q^{11} + q^{12} + q^{13} + 2q^{14} + q^{16} - 8q^{17} - q^{18} - 6q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 