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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 120240.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
120240.n1 | 120240by2 | \([0, 0, 0, -54796323, -158513412958]\) | \(-6093832136609347161121/108676727597808690\) | \(-324506969779415183400960\) | \([]\) | \(12644352\) | \(3.3081\) | |
120240.n2 | 120240by1 | \([0, 0, 0, -213123, 163336322]\) | \(-358531401121921/3652290000000\) | \(-10905679503360000000\) | \([]\) | \(1806336\) | \(2.3352\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 120240.n have rank \(1\).
Complex multiplication
The elliptic curves in class 120240.n do not have complex multiplication.Modular form 120240.2.a.n
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.