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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 38646m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38646.j2 | 38646m1 | \([1, -1, 0, -14643, 702837]\) | \(-476324646618673/14036502016\) | \(-10232609969664\) | \([]\) | \(151200\) | \(1.2751\) | \(\Gamma_0(N)\)-optimal |
38646.j1 | 38646m2 | \([1, -1, 0, -1194363, 502702173]\) | \(-258467184041747339953/6200536\) | \(-4520190744\) | \([3]\) | \(453600\) | \(1.8244\) |
Rank
sage: E.rank()
The elliptic curves in class 38646m have rank \(1\).
Complex multiplication
The elliptic curves in class 38646m do not have complex multiplication.Modular form 38646.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.