# Properties

 Label 2310.t Number of curves $4$ Conductor $2310$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 2310.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2310.t1 2310u3 $$[1, 0, 0, -24261, -1456515]$$ $$1579250141304807889/41926500$$ $$41926500$$ $$[2]$$ $$5184$$ $$0.97671$$
2310.t2 2310u4 $$[1, 0, 0, -24231, -1460289]$$ $$-1573398910560073969/8138108343750$$ $$-8138108343750$$ $$[2]$$ $$10368$$ $$1.3233$$
2310.t3 2310u1 $$[1, 0, 0, -321, -1719]$$ $$3658671062929/880165440$$ $$880165440$$ $$[6]$$ $$1728$$ $$0.42740$$ $$\Gamma_0(N)$$-optimal
2310.t4 2310u2 $$[1, 0, 0, 759, -10575]$$ $$48351870250991/76871856600$$ $$-76871856600$$ $$[6]$$ $$3456$$ $$0.77398$$

## Rank

sage: E.rank()

The elliptic curves in class 2310.t have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2310.t do not have complex multiplication.

## Modular form2310.2.a.t

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} - q^{11} + q^{12} - 4 q^{13} + q^{14} - q^{15} + q^{16} + q^{18} + 8 q^{19} + O(q^{20})$$

## 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.