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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 28050c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28050.q2 | 28050c1 | \([1, 1, 0, -22000, 544000]\) | \(75370704203521/35157196800\) | \(549331200000000\) | \([2]\) | \(129024\) | \(1.5228\) | \(\Gamma_0(N)\)-optimal |
28050.q1 | 28050c2 | \([1, 1, 0, -294000, 61200000]\) | \(179865548102096641/119964240000\) | \(1874441250000000\) | \([2]\) | \(258048\) | \(1.8693\) |
Rank
sage: E.rank()
The elliptic curves in class 28050c have rank \(1\).
Complex multiplication
The elliptic curves in class 28050c do not have complex multiplication.Modular form 28050.2.a.c
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.