# Properties

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

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

sage: E.isogeny_class()

## Elliptic curves in class 1950.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.i1 1950j2 $$[1, 0, 1, -66, 178]$$ $$248858189/27378$$ $$3422250$$ $$$$ $$512$$ $$-0.012751$$
1950.i2 1950j1 $$[1, 0, 1, -16, -22]$$ $$3307949/468$$ $$58500$$ $$$$ $$256$$ $$-0.35932$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1950.2.a.i

sage: E.q_eigenform(10)

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