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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 22848.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22848.z1 | 22848bt4 | \([0, -1, 0, -506497, -119621183]\) | \(438536015880092936/64602489661101\) | \(2116894381214957568\) | \([2]\) | \(294912\) | \(2.2411\) | |
| 22848.z2 | 22848bt2 | \([0, -1, 0, -136057, 17515705]\) | \(68003243639904448/7163272192041\) | \(29340762898599936\) | \([2, 2]\) | \(147456\) | \(1.8946\) | |
| 22848.z3 | 22848bt1 | \([0, -1, 0, -132412, 18589522]\) | \(4011705594213827392/52680152007\) | \(3371529728448\) | \([2]\) | \(73728\) | \(1.5480\) | \(\Gamma_0(N)\)-optimal |
| 22848.z4 | 22848bt3 | \([0, -1, 0, 176063, 85869985]\) | \(18419405270942584/108003564029403\) | \(-3539060786115477504\) | \([2]\) | \(294912\) | \(2.2411\) |
Rank
sage: E.rank()
The elliptic curves in class 22848.z have rank \(0\).
Complex multiplication
The elliptic curves in class 22848.z do not have complex multiplication.Modular form 22848.2.a.z
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.
