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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 247938.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
247938.p1 | 247938p2 | \([1, 1, 1, -57564881, 168102454067]\) | \(-23769846831649063249/3261823333284\) | \(-2894880215061239818404\) | \([]\) | \(32598720\) | \(3.1359\) | |
247938.p2 | 247938p1 | \([1, 1, 1, 152779, -51288613]\) | \(444369620591/1540767744\) | \(-1367437044366065664\) | \([]\) | \(4656960\) | \(2.1630\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 247938.p have rank \(1\).
Complex multiplication
The elliptic curves in class 247938.p do not have complex multiplication.Modular form 247938.2.a.p
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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.