# Properties

 Label 115920.t Number of curves $2$ Conductor $115920$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 115920.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.t1 115920cb1 $$[0, 0, 0, -709430643, -3040869636558]$$ $$489781415227546051766883/233890092903563264000$$ $$18856586029550943130877952000$$ $$[2]$$ $$74317824$$ $$4.1194$$ $$\Gamma_0(N)$$-optimal
115920.t2 115920cb2 $$[0, 0, 0, 2546397837, -23128680192462]$$ $$22649115256119592694355357/15973509811739648000000$$ $$-1287809407485835229528064000000$$ $$[2]$$ $$148635648$$ $$4.4660$$

## Rank

sage: E.rank()

The elliptic curves in class 115920.t have rank $$1$$.

## Complex multiplication

The elliptic curves in class 115920.t do not have complex multiplication.

## Modular form 115920.2.a.t

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} + 2q^{11} - 6q^{13} + 6q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.