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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 155526dg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155526.p2 | 155526dg1 | \([1, 1, 0, -130551656, 573971889408]\) | \(50489872297/12096\) | \(58953335024601455167296\) | \([]\) | \(26707968\) | \(3.3586\) | \(\Gamma_0(N)\)-optimal |
155526.p1 | 155526dg2 | \([1, 1, 0, -336234791, -1608943222347]\) | \(862551551257/269746176\) | \(1314685572530845606432997376\) | \([]\) | \(80123904\) | \(3.9079\) |
Rank
sage: E.rank()
The elliptic curves in class 155526dg have rank \(1\).
Complex multiplication
The elliptic curves in class 155526dg do not have complex multiplication.Modular form 155526.2.a.dg
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.