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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 390.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
390.f1 | 390b5 | \([1, 1, 1, -9015, -333213]\) | \(81025909800741361/11088090\) | \(11088090\) | \([2]\) | \(512\) | \(0.76407\) | |
390.f2 | 390b4 | \([1, 1, 1, -845, 9095]\) | \(66730743078481/60937500\) | \(60937500\) | \([4]\) | \(256\) | \(0.41750\) | |
390.f3 | 390b3 | \([1, 1, 1, -565, -5353]\) | \(19948814692561/231344100\) | \(231344100\) | \([2, 2]\) | \(256\) | \(0.41750\) | |
390.f4 | 390b6 | \([1, 1, 1, -115, -13093]\) | \(-168288035761/73415764890\) | \(-73415764890\) | \([2]\) | \(512\) | \(0.76407\) | |
390.f5 | 390b2 | \([1, 1, 1, -65, 47]\) | \(30400540561/15210000\) | \(15210000\) | \([2, 4]\) | \(128\) | \(0.070926\) | |
390.f6 | 390b1 | \([1, 1, 1, 15, 15]\) | \(371694959/249600\) | \(-249600\) | \([4]\) | \(64\) | \(-0.27565\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 390.f have rank \(0\).
Complex multiplication
The elliptic curves in class 390.f do not have complex multiplication.Modular form 390.2.a.f
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.