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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 30926b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30926.c1 | 30926b1 | \([1, -1, 0, -27493628, -15008057520]\) | \(2053710181431/1101463552\) | \(1232681426055214200848384\) | \([2]\) | \(5053440\) | \(3.3138\) | \(\Gamma_0(N)\)-optimal |
30926.c2 | 30926b2 | \([1, -1, 0, 105399812, -117787844016]\) | \(115707762924489/72313663744\) | \(-80928424717617129193979648\) | \([2]\) | \(10106880\) | \(3.6604\) |
Rank
sage: E.rank()
The elliptic curves in class 30926b have rank \(0\).
Complex multiplication
The elliptic curves in class 30926b do not have complex multiplication.Modular form 30926.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.