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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 350064.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
350064.m1 | 350064m4 | \([0, 0, 0, -6054051, -5731498654]\) | \(8218157522273610913/3262914972603\) | \(9743011901552996352\) | \([2]\) | \(7864320\) | \(2.6077\) | |
350064.m2 | 350064m3 | \([0, 0, 0, -3215811, 2177307650]\) | \(1231708064988053953/26933399479701\) | \(80422699911995510784\) | \([4]\) | \(7864320\) | \(2.6077\) | |
350064.m3 | 350064m2 | \([0, 0, 0, -435891, -60527950]\) | \(3067396672113073/1245074357241\) | \(3717772109531910144\) | \([2, 2]\) | \(3932160\) | \(2.2611\) | |
350064.m4 | 350064m1 | \([0, 0, 0, 88989, -6885214]\) | \(26100282937247/21962862207\) | \(-65580755144306688\) | \([2]\) | \(1966080\) | \(1.9145\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 350064.m have rank \(1\).
Complex multiplication
The elliptic curves in class 350064.m do not have complex multiplication.Modular form 350064.2.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.