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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 246b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
246.g2 | 246b1 | \([1, 0, 0, -175, -27847]\) | \(-592915705201/334302806016\) | \(-334302806016\) | \([5]\) | \(300\) | \(0.89036\) | \(\Gamma_0(N)\)-optimal |
246.g1 | 246b2 | \([1, 0, 0, -579535, -169860007]\) | \(-21525971829968662032241/11122195296\) | \(-11122195296\) | \([]\) | \(1500\) | \(1.6951\) |
Rank
sage: E.rank()
The elliptic curves in class 246b have rank \(0\).
Complex multiplication
The elliptic curves in class 246b do not have complex multiplication.Modular form 246.2.a.b
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.