# Properties

 Label 1950.t Number of curves $2$ Conductor $1950$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 1950.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.t1 1950o2 $$[1, 1, 1, -3363, -76479]$$ $$-168256703745625/30371328$$ $$-759283200$$ $$[]$$ $$1944$$ $$0.70771$$
1950.t2 1950o1 $$[1, 1, 1, 12, -339]$$ $$7604375/2047032$$ $$-51175800$$ $$[]$$ $$648$$ $$0.15840$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1950.2.a.t

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} + 4q^{7} + q^{8} + q^{9} - q^{12} - q^{13} + 4q^{14} + q^{16} + q^{18} + 5q^{19} + O(q^{20})$$ ## 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. 