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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 184093m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
184093.m1 | 184093m1 | \([1, 1, 0, -842874, -298165993]\) | \(23320116793/2873\) | \(8158632937222313\) | \([2]\) | \(2488320\) | \(2.0765\) | \(\Gamma_0(N)\)-optimal |
184093.m2 | 184093m2 | \([1, 1, 0, -772069, -350235990]\) | \(-17923019113/8254129\) | \(-23439752428639705249\) | \([2]\) | \(4976640\) | \(2.4231\) |
Rank
sage: E.rank()
The elliptic curves in class 184093m have rank \(1\).
Complex multiplication
The elliptic curves in class 184093m do not have complex multiplication.Modular form 184093.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.