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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 38440.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38440.h1 | 38440k4 | \([0, 0, 0, -79442987, 272540758966]\) | \(61012706050976004/3875\) | \(3521614606208000\) | \([4]\) | \(1658880\) | \(2.8895\) | |
| 38440.h2 | 38440k2 | \([0, 0, 0, -4965487, 4257908466]\) | \(59593532744016/15015625\) | \(3411564149764000000\) | \([2, 2]\) | \(829440\) | \(2.5429\) | |
| 38440.h3 | 38440k3 | \([0, 0, 0, -4369667, 5318110574]\) | \(-10153098934884/7568359375\) | \(-6878153527750000000000\) | \([2]\) | \(1658880\) | \(2.8895\) | |
| 38440.h4 | 38440k1 | \([0, 0, 0, -347882, 49423269]\) | \(327890958336/115440125\) | \(1639256573961602000\) | \([2]\) | \(414720\) | \(2.1963\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38440.h have rank \(0\).
Complex multiplication
The elliptic curves in class 38440.h do not have complex multiplication.Modular form 38440.2.a.h
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
