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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 2320.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2320.a1 | 2320c2 | \([0, 1, 0, -156, 700]\) | \(1650587344/725\) | \(185600\) | \([2]\) | \(512\) | \(-0.029974\) | |
| 2320.a2 | 2320c1 | \([0, 1, 0, -11, 4]\) | \(10061824/4205\) | \(67280\) | \([2]\) | \(256\) | \(-0.37655\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2320.a have rank \(1\).
Complex multiplication
The elliptic curves in class 2320.a do not have complex multiplication.Modular form 2320.2.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.
