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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 57330.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57330.u1 | 57330p2 | \([1, -1, 0, -339879150, 2411849487060]\) | \(-1033202467754104941601/6178315520\) | \(-25964617666760398080\) | \([3]\) | \(7983360\) | \(3.3339\) | |
| 57330.u2 | 57330p1 | \([1, -1, 0, -4013550, 3610156500]\) | \(-1701366814932001/354418688000\) | \(-1489458687903793152000\) | \([]\) | \(2661120\) | \(2.7846\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 57330.u have rank \(1\).
Complex multiplication
The elliptic curves in class 57330.u do not have complex multiplication.Modular form 57330.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
