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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 726h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 726.i3 | 726h1 | \([1, 0, 0, -668, -6324]\) | \(18609625/1188\) | \(2104614468\) | \([2]\) | \(480\) | \(0.53956\) | \(\Gamma_0(N)\)-optimal |
| 726.i4 | 726h2 | \([1, 0, 0, 542, -26410]\) | \(9938375/176418\) | \(-312535248498\) | \([2]\) | \(960\) | \(0.88614\) | |
| 726.i1 | 726h3 | \([1, 0, 0, -9743, 367929]\) | \(57736239625/255552\) | \(452725956672\) | \([2]\) | \(1440\) | \(1.0889\) | |
| 726.i2 | 726h4 | \([1, 0, 0, -4903, 734801]\) | \(-7357983625/127552392\) | \(-225966843123912\) | \([2]\) | \(2880\) | \(1.4354\) |
Rank
sage: E.rank()
The elliptic curves in class 726h have rank \(0\).
Complex multiplication
The elliptic curves in class 726h do not have complex multiplication.Modular form 726.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
