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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 42483y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42483.bb2 | 42483y1 | \([0, 1, 1, 80246, 4536109]\) | \(4096/3\) | \(-41855235245986659\) | \([]\) | \(587520\) | \(1.8777\) | \(\Gamma_0(N)\)-optimal |
42483.bb1 | 42483y2 | \([0, 1, 1, -11956604, 15909548225]\) | \(-13549359104/243\) | \(-3390274054924919379\) | \([]\) | \(2937600\) | \(2.6824\) |
Rank
sage: E.rank()
The elliptic curves in class 42483y have rank \(1\).
Complex multiplication
The elliptic curves in class 42483y do not have complex multiplication.Modular form 42483.2.a.y
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.