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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 22848.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22848.m1 | 22848m4 | \([0, -1, 0, -19649, -1053567]\) | \(25604555308424/1102059\) | \(36112269312\) | \([2]\) | \(43008\) | \(1.1048\) | |
22848.m2 | 22848m3 | \([0, -1, 0, -6049, 169345]\) | \(747130257224/63241479\) | \(2072296783872\) | \([2]\) | \(43008\) | \(1.1048\) | |
22848.m3 | 22848m2 | \([0, -1, 0, -1289, -14391]\) | \(57870788032/10323369\) | \(42284519424\) | \([2, 2]\) | \(21504\) | \(0.75828\) | |
22848.m4 | 22848m1 | \([0, -1, 0, 156, -1386]\) | \(6518244032/15785469\) | \(-1010270016\) | \([2]\) | \(10752\) | \(0.41170\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22848.m have rank \(0\).
Complex multiplication
The elliptic curves in class 22848.m do not have complex multiplication.Modular form 22848.2.a.m
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.