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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 28050dd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28050.dd2 | 28050dd1 | \([1, 0, 0, -290563, -60008383]\) | \(173629978755828841/1000026931200\) | \(15625420800000000\) | \([2]\) | \(337920\) | \(1.9484\) | \(\Gamma_0(N)\)-optimal |
28050.dd1 | 28050dd2 | \([1, 0, 0, -4642563, -3850600383]\) | \(708234550511150304361/23696640000\) | \(370260000000000\) | \([2]\) | \(675840\) | \(2.2950\) |
Rank
sage: E.rank()
The elliptic curves in class 28050dd have rank \(0\).
Complex multiplication
The elliptic curves in class 28050dd do not have complex multiplication.Modular form 28050.2.a.dd
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.