# Properties

 Label 1950.o Number of curves $4$ Conductor $1950$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 1950.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.o1 1950n4 $$[1, 1, 1, -21814438, -39224901469]$$ $$73474353581350183614361/576510977802240$$ $$9007984028160000000$$ $$$$ $$103680$$ $$2.8101$$
1950.o2 1950n3 $$[1, 1, 1, -1334438, -640581469]$$ $$-16818951115904497561/1592332281446400$$ $$-24880191897600000000$$ $$$$ $$51840$$ $$2.4635$$
1950.o3 1950n2 $$[1, 1, 1, -400063, 3499781]$$ $$453198971846635561/261896250564000$$ $$4092128915062500000$$ $$$$ $$34560$$ $$2.2608$$
1950.o4 1950n1 $$[1, 1, 1, 99937, 499781]$$ $$7064514799444439/4094064000000$$ $$-63969750000000000$$ $$$$ $$17280$$ $$1.9142$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1950.o have rank $$0$$.

## Complex multiplication

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

## Modular form1950.2.a.o

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 