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SageMath
E = EllipticCurve("fi1")
E.isogeny_class()
Elliptic curves in class 46800.fi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46800.fi1 | 46800eh4 | \([0, 0, 0, -311502675, 2116122399250]\) | \(71647584155243142409/10140000\) | \(473091840000000000\) | \([2]\) | \(5898240\) | \(3.2444\) | |
46800.fi2 | 46800eh3 | \([0, 0, 0, -22350675, 22635423250]\) | \(26465989780414729/10571870144160\) | \(493241173445928960000000\) | \([2]\) | \(5898240\) | \(3.2444\) | |
46800.fi3 | 46800eh2 | \([0, 0, 0, -19470675, 33058143250]\) | \(17496824387403529/6580454400\) | \(307017680486400000000\) | \([2, 2]\) | \(2949120\) | \(2.8979\) | |
46800.fi4 | 46800eh1 | \([0, 0, 0, -1038675, 673119250]\) | \(-2656166199049/2658140160\) | \(-124018187304960000000\) | \([2]\) | \(1474560\) | \(2.5513\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46800.fi have rank \(0\).
Complex multiplication
The elliptic curves in class 46800.fi do not have complex multiplication.Modular form 46800.2.a.fi
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.