Properties

 Label 452400m Number of curves $4$ Conductor $452400$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

Elliptic curves in class 452400m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
452400.m3 452400m1 $$[0, -1, 0, -709008, -229543488]$$ $$615882348586441/21715200$$ $$1389772800000000$$ $$$$ $$7077888$$ $$1.9955$$ $$\Gamma_0(N)$$-optimal*
452400.m2 452400m2 $$[0, -1, 0, -741008, -207655488]$$ $$703093388853961/115124490000$$ $$7367967360000000000$$ $$[2, 2]$$ $$14155776$$ $$2.3420$$ $$\Gamma_0(N)$$-optimal*
452400.m1 452400m3 $$[0, -1, 0, -3341008, 2153144512]$$ $$64443098670429961/6032611833300$$ $$386087157331200000000$$ $$$$ $$28311552$$ $$2.6886$$ $$\Gamma_0(N)$$-optimal*
452400.m4 452400m4 $$[0, -1, 0, 1346992, -1168135488]$$ $$4223169036960119/11647532812500$$ $$-745442100000000000000$$ $$$$ $$28311552$$ $$2.6886$$
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 452400m1.

Rank

sage: E.rank()

The elliptic curves in class 452400m have rank $$1$$.

Complex multiplication

The elliptic curves in class 452400m do not have complex multiplication.

Modular form 452400.2.a.m

sage: E.q_eigenform(10)

$$q - q^{3} - 4 q^{7} + q^{9} + 4 q^{11} - q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})$$ 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 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. 