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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 19800a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19800.bo2 | 19800a1 | \([0, 0, 0, -375, 2250]\) | \(54000/11\) | \(1188000000\) | \([2]\) | \(9216\) | \(0.45691\) | \(\Gamma_0(N)\)-optimal |
| 19800.bo1 | 19800a2 | \([0, 0, 0, -1875, -29250]\) | \(1687500/121\) | \(52272000000\) | \([2]\) | \(18432\) | \(0.80348\) |
Rank
sage: E.rank()
The elliptic curves in class 19800a have rank \(0\).
Complex multiplication
The elliptic curves in class 19800a do not have complex multiplication.Modular form 19800.2.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 Cremona 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 Cremona labels.
