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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 14700.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14700.u1 | 14700e1 | \([0, -1, 0, -4975133, -2838221238]\) | \(463030539649024/149501953125\) | \(4397188820800781250000\) | \([2]\) | \(967680\) | \(2.8564\) | \(\Gamma_0(N)\)-optimal |
14700.u2 | 14700e2 | \([0, -1, 0, 14165492, -19414002488]\) | \(667990736021936/732392128125\) | \(-344660805927112500000000\) | \([2]\) | \(1935360\) | \(3.2030\) |
Rank
sage: E.rank()
The elliptic curves in class 14700.u have rank \(1\).
Complex multiplication
The elliptic curves in class 14700.u do not have complex multiplication.Modular form 14700.2.a.u
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.