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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 397800.cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
397800.cb1 | 397800cb3 | \([0, 0, 0, -14061675, 20295521750]\) | \(26362547147244676/244298925\) | \(2849502661200000000\) | \([2]\) | \(14155776\) | \(2.7048\) | |
397800.cb2 | 397800cb2 | \([0, 0, 0, -899175, 301684250]\) | \(27572037674704/2472575625\) | \(7210030522500000000\) | \([2, 2]\) | \(7077888\) | \(2.3582\) | |
397800.cb3 | 397800cb1 | \([0, 0, 0, -196050, -28081375]\) | \(4572531595264/776953125\) | \(141599707031250000\) | \([2]\) | \(3538944\) | \(2.0117\) | \(\Gamma_0(N)\)-optimal |
397800.cb4 | 397800cb4 | \([0, 0, 0, 1013325, 1412846750]\) | \(9865576607324/79640206425\) | \(-928923367741200000000\) | \([2]\) | \(14155776\) | \(2.7048\) |
Rank
sage: E.rank()
The elliptic curves in class 397800.cb have rank \(1\).
Complex multiplication
The elliptic curves in class 397800.cb do not have complex multiplication.Modular form 397800.2.a.cb
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.