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SageMath
E = EllipticCurve("hl1")
E.isogeny_class()
Elliptic curves in class 377520hl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
377520.hl2 | 377520hl1 | \([0, 1, 0, 87080, -10432732]\) | \(40254822716/49359375\) | \(-89541779184000000\) | \([2]\) | \(2457600\) | \(1.9389\) | \(\Gamma_0(N)\)-optimal |
377520.hl1 | 377520hl2 | \([0, 1, 0, -517920, -100698732]\) | \(4234737878642/1247410125\) | \(4525799687076096000\) | \([2]\) | \(4915200\) | \(2.2855\) |
Rank
sage: E.rank()
The elliptic curves in class 377520hl have rank \(1\).
Complex multiplication
The elliptic curves in class 377520hl do not have complex multiplication.Modular form 377520.2.a.hl
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.