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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 5796.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5796.a1 | 5796b2 | \([0, 0, 0, -37887, -2836570]\) | \(870143011569648/671898241\) | \(4644160641792\) | \([2]\) | \(20736\) | \(1.3623\) | |
| 5796.a2 | 5796b1 | \([0, 0, 0, -1872, -63415]\) | \(-1679412953088/3049579729\) | \(-1317418442928\) | \([2]\) | \(10368\) | \(1.0157\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5796.a have rank \(1\).
Complex multiplication
The elliptic curves in class 5796.a do not have complex multiplication.Modular form 5796.2.a.a
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.
