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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 84150.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84150.u1 | 84150bv2 | \([1, -1, 0, -154692, -23125784]\) | \(35940267099001/448014600\) | \(5103166303125000\) | \([2]\) | \(884736\) | \(1.8237\) | |
| 84150.u2 | 84150bv1 | \([1, -1, 0, -1692, -940784]\) | \(-47045881/33570240\) | \(-382386015000000\) | \([2]\) | \(442368\) | \(1.4772\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 84150.u have rank \(1\).
Complex multiplication
The elliptic curves in class 84150.u do not have complex multiplication.Modular form 84150.2.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.
