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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 357390.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
357390.b1 | 357390b3 | \([1, -1, 0, -5206590, 4574021400]\) | \(455129268177961/4392300\) | \(150640285251782700\) | \([2]\) | \(12386304\) | \(2.4575\) | |
357390.b2 | 357390b2 | \([1, -1, 0, -333090, 67983300]\) | \(119168121961/10890000\) | \(373488310541610000\) | \([2, 2]\) | \(6193152\) | \(2.1109\) | |
357390.b3 | 357390b1 | \([1, -1, 0, -73170, -6405804]\) | \(1263214441/211200\) | \(7243409658988800\) | \([2]\) | \(3096576\) | \(1.7644\) | \(\Gamma_0(N)\)-optimal |
357390.b4 | 357390b4 | \([1, -1, 0, 381690, 319728816]\) | \(179310732119/1392187500\) | \(-47747085154467187500\) | \([2]\) | \(12386304\) | \(2.4575\) |
Rank
sage: E.rank()
The elliptic curves in class 357390.b have rank \(1\).
Complex multiplication
The elliptic curves in class 357390.b do not have complex multiplication.Modular form 357390.2.a.b
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.