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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 78400.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 78400.u1 | 78400dk1 | \([0, 0, 0, -210700, -37226000]\) | \(-5154200289/20\) | \(-4014080000000\) | \([]\) | \(552960\) | \(1.6316\) | \(\Gamma_0(N)\)-optimal |
| 78400.u2 | 78400dk2 | \([0, 0, 0, 1469300, 353206000]\) | \(1747829720511/1280000000\) | \(-256901120000000000000\) | \([]\) | \(3870720\) | \(2.6046\) |
Rank
sage: E.rank()
The elliptic curves in class 78400.u have rank \(0\).
Complex multiplication
The elliptic curves in class 78400.u do not have complex multiplication.Modular form 78400.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
