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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 274890.cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
274890.cb1 | 274890cb4 | \([1, 0, 1, -18468469, -29645136958]\) | \(5921450764096952391481/200074809015963750\) | \(23538601205919119223750\) | \([2]\) | \(28311552\) | \(3.0651\) | |
274890.cb2 | 274890cb2 | \([1, 0, 1, -2849719, 1211265542]\) | \(21754112339458491481/7199734626562500\) | \(847041579080451562500\) | \([2, 2]\) | \(14155776\) | \(2.7185\) | |
274890.cb3 | 274890cb1 | \([1, 0, 1, -2566499, 1582057166]\) | \(15891267085572193561/3334993530000\) | \(392358653810970000\) | \([2]\) | \(7077888\) | \(2.3719\) | \(\Gamma_0(N)\)-optimal |
274890.cb4 | 274890cb3 | \([1, 0, 1, 8237511, 8338136986]\) | \(525440531549759128199/559322204589843750\) | \(-65803698047790527343750\) | \([2]\) | \(28311552\) | \(3.0651\) |
Rank
sage: E.rank()
The elliptic curves in class 274890.cb have rank \(1\).
Complex multiplication
The elliptic curves in class 274890.cb do not have complex multiplication.Modular form 274890.2.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.