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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 366b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
366.f2 | 366b1 | \([1, 0, 0, -5, 33]\) | \(-13997521/474336\) | \(-474336\) | \([5]\) | \(60\) | \(-0.23056\) | \(\Gamma_0(N)\)-optimal |
366.f1 | 366b2 | \([1, 0, 0, -515, -5697]\) | \(-15107691357361/5067577806\) | \(-5067577806\) | \([]\) | \(300\) | \(0.57416\) |
Rank
sage: E.rank()
The elliptic curves in class 366b have rank \(0\).
Complex multiplication
The elliptic curves in class 366b do not have complex multiplication.Modular form 366.2.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.