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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 60984bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
60984.bx1 | 60984bp1 | \([0, 0, 0, -6534, 179685]\) | \(55296/7\) | \(3905399138256\) | \([2]\) | \(103680\) | \(1.1453\) | \(\Gamma_0(N)\)-optimal |
60984.bx2 | 60984bp2 | \([0, 0, 0, 9801, 934362]\) | \(11664/49\) | \(-437404703484672\) | \([2]\) | \(207360\) | \(1.4919\) |
Rank
sage: E.rank()
The elliptic curves in class 60984bp have rank \(1\).
Complex multiplication
The elliptic curves in class 60984bp do not have complex multiplication.Modular form 60984.2.a.bp
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.