Properties

 Label 1800.m Number of curves 6 Conductor 1800 CM no Rank 1 Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1800.m1")

sage: E.isogeny_class()

Elliptic curves in class 1800.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1800.m1 1800s5 [0, 0, 0, -86475, 9787750] [2] 4096
1800.m2 1800s3 [0, 0, 0, -14475, -670250] [2] 2048
1800.m3 1800s4 [0, 0, 0, -5475, 148750] [2, 2] 2048
1800.m4 1800s2 [0, 0, 0, -975, -8750] [2, 2] 1024
1800.m5 1800s1 [0, 0, 0, 150, -875] [2] 512 $$\Gamma_0(N)$$-optimal
1800.m6 1800s6 [0, 0, 0, 3525, 589750] [2] 4096

Rank

sage: E.rank()

The elliptic curves in class 1800.m have rank $$1$$.

Modular form1800.2.a.m

sage: E.q_eigenform(10)

$$q - 4q^{11} + 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.