# Properties

 Label 62400.t Number of curves $4$ Conductor $62400$ CM no Rank $1$ Graph # Learn more about

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

sage: E.isogeny_class()

## Elliptic curves in class 62400.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.t1 62400fg4 $$[0, -1, 0, -165633, 25903137]$$ $$490757540836/2142075$$ $$2193484800000000$$ $$$$ $$589824$$ $$1.7966$$
62400.t2 62400fg2 $$[0, -1, 0, -15633, -46863]$$ $$1650587344/950625$$ $$243360000000000$$ $$[2, 2]$$ $$294912$$ $$1.4500$$
62400.t3 62400fg1 $$[0, -1, 0, -11133, -447363]$$ $$9538484224/26325$$ $$421200000000$$ $$$$ $$147456$$ $$1.1035$$ $$\Gamma_0(N)$$-optimal
62400.t4 62400fg3 $$[0, -1, 0, 62367, -436863]$$ $$26198797244/15234375$$ $$-15600000000000000$$ $$$$ $$589824$$ $$1.7966$$

## Rank

sage: E.rank()

The elliptic curves in class 62400.t have rank $$1$$.

## Complex multiplication

The elliptic curves in class 62400.t do not have complex multiplication.

## Modular form 62400.2.a.t

sage: E.q_eigenform(10)

$$q - q^{3} - 4q^{7} + q^{9} + 4q^{11} + q^{13} + 6q^{17} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 