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SageMath
E = EllipticCurve("ee1")
E.isogeny_class()
Elliptic curves in class 46800.ee
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46800.ee1 | 46800dc4 | \([0, 0, 0, -4305675, -3263831750]\) | \(189208196468929/10860320250\) | \(506699101584000000000\) | \([2]\) | \(1327104\) | \(2.7270\) | |
46800.ee2 | 46800dc2 | \([0, 0, 0, -741675, 244764250]\) | \(967068262369/4928040\) | \(229922634240000000\) | \([2]\) | \(442368\) | \(2.1777\) | |
46800.ee3 | 46800dc1 | \([0, 0, 0, -21675, 7884250]\) | \(-24137569/561600\) | \(-26202009600000000\) | \([2]\) | \(221184\) | \(1.8311\) | \(\Gamma_0(N)\)-optimal |
46800.ee4 | 46800dc3 | \([0, 0, 0, 194325, -208331750]\) | \(17394111071/411937500\) | \(-19219356000000000000\) | \([2]\) | \(663552\) | \(2.3804\) |
Rank
sage: E.rank()
The elliptic curves in class 46800.ee have rank \(1\).
Complex multiplication
The elliptic curves in class 46800.ee do not have complex multiplication.Modular form 46800.2.a.ee
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.