# Properties

 Label 124950t Number of curves $4$ Conductor $124950$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 124950t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
124950.bb4 124950t1 $$[1, 1, 0, 1200, -4320000]$$ $$103823/4386816$$ $$-8064133056000000$$ $$[2]$$ $$1179648$$ $$1.7311$$ $$\Gamma_0(N)$$-optimal
124950.bb3 124950t2 $$[1, 1, 0, -390800, -92520000]$$ $$3590714269297/73410624$$ $$134948226609000000$$ $$[2, 2]$$ $$2359296$$ $$2.0777$$
124950.bb2 124950t3 $$[1, 1, 0, -831800, 153999000]$$ $$34623662831857/14438442312$$ $$26541692180695125000$$ $$[2]$$ $$4718592$$ $$2.4242$$
124950.bb1 124950t4 $$[1, 1, 0, -6221800, -5975999000]$$ $$14489843500598257/6246072$$ $$11481939448875000$$ $$[2]$$ $$4718592$$ $$2.4242$$

## Rank

sage: E.rank()

The elliptic curves in class 124950t have rank $$1$$.

## Complex multiplication

The elliptic curves in class 124950t do not have complex multiplication.

## Modular form 124950.2.a.t

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - q^{12} - 6q^{13} + q^{16} + q^{17} - q^{18} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.