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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 111090.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111090.n1 | 111090p4 | \([1, 1, 0, -66465422, -116975783364]\) | \(219353215817909485369/87028564162480920\) | \(12883350864186403437737880\) | \([2]\) | \(38928384\) | \(3.5165\) | |
111090.n2 | 111090p2 | \([1, 1, 0, -30176022, 62504331156]\) | \(20527812941011798969/474091398849600\) | \(70182541695954113294400\) | \([2, 2]\) | \(19464192\) | \(3.1699\) | |
111090.n3 | 111090p1 | \([1, 1, 0, -30006742, 63254343124]\) | \(20184279492242626489/11148103680\) | \(1650319438932971520\) | \([2]\) | \(9732096\) | \(2.8233\) | \(\Gamma_0(N)\)-optimal |
111090.n4 | 111090p3 | \([1, 1, 0, 3404898, 193987065324]\) | \(29489595518609351/109830613939935000\) | \(-16258872574014070327215000\) | \([2]\) | \(38928384\) | \(3.5165\) |
Rank
sage: E.rank()
The elliptic curves in class 111090.n have rank \(0\).
Complex multiplication
The elliptic curves in class 111090.n do not have complex multiplication.Modular form 111090.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.