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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 271440.cd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
271440.cd1 | 271440cd4 | \([0, 0, 0, -1202763, -464838662]\) | \(64443098670429961/6032611833300\) | \(18013282412444467200\) | \([2]\) | \(9437184\) | \(2.4332\) | |
271440.cd2 | 271440cd2 | \([0, 0, 0, -266763, 44906938]\) | \(703093388853961/115124490000\) | \(343759885148160000\) | \([2, 2]\) | \(4718592\) | \(2.0866\) | |
271440.cd3 | 271440cd1 | \([0, 0, 0, -255243, 49632442]\) | \(615882348586441/21715200\) | \(64841239756800\) | \([2]\) | \(2359296\) | \(1.7400\) | \(\Gamma_0(N)\)-optimal |
271440.cd4 | 271440cd3 | \([0, 0, 0, 484917, 252220282]\) | \(4223169036960119/11647532812500\) | \(-34779346617600000000\) | \([2]\) | \(9437184\) | \(2.4332\) |
Rank
sage: E.rank()
The elliptic curves in class 271440.cd have rank \(0\).
Complex multiplication
The elliptic curves in class 271440.cd do not have complex multiplication.Modular form 271440.2.a.cd
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.