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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 165620m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
165620.g1 | 165620m1 | \([0, -1, 0, -8250636, -9124557560]\) | \(-177953104/125\) | \(-43630530372814112000\) | \([]\) | \(6967296\) | \(2.7048\) | \(\Gamma_0(N)\)-optimal |
165620.g2 | 165620m2 | \([0, -1, 0, 7980124, -38768417624]\) | \(161017136/1953125\) | \(-681727037075220500000000\) | \([]\) | \(20901888\) | \(3.2541\) |
Rank
sage: E.rank()
The elliptic curves in class 165620m have rank \(1\).
Complex multiplication
The elliptic curves in class 165620m do not have complex multiplication.Modular form 165620.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.