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SageMath
E = EllipticCurve("ed1")
E.isogeny_class()
Elliptic curves in class 229320.ed
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
229320.ed1 | 229320dg1 | \([0, 0, 0, -4560087, -1464657334]\) | \(477625344356176/234195040625\) | \(5142016049111978400000\) | \([2]\) | \(14745600\) | \(2.8593\) | \(\Gamma_0(N)\)-optimal |
229320.ed2 | 229320dg2 | \([0, 0, 0, 16616733, -11218700626]\) | \(5777565954713276/3962587890625\) | \(-348012331520490000000000\) | \([2]\) | \(29491200\) | \(3.2058\) |
Rank
sage: E.rank()
The elliptic curves in class 229320.ed have rank \(0\).
Complex multiplication
The elliptic curves in class 229320.ed do not have complex multiplication.Modular form 229320.2.a.ed
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.