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SageMath
E = EllipticCurve("hj1")
E.isogeny_class()
Elliptic curves in class 47040.hj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47040.hj1 | 47040dq2 | \([0, 1, 0, -294065, 38734863]\) | \(4253563312/1476225\) | \(976011321238732800\) | \([2]\) | \(860160\) | \(2.1535\) | |
| 47040.hj2 | 47040dq1 | \([0, 1, 0, -122565, -16110837]\) | \(4927700992/151875\) | \(6275792960640000\) | \([2]\) | \(430080\) | \(1.8069\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47040.hj have rank \(0\).
Complex multiplication
The elliptic curves in class 47040.hj do not have complex multiplication.Modular form 47040.2.a.hj
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.
