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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 88935bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88935.o2 | 88935bc1 | \([1, 1, 1, -1074620, 409016180]\) | \(876440017817099/44659644435\) | \(6993290298325442265\) | \([2]\) | \(1935360\) | \(2.3741\) | \(\Gamma_0(N)\)-optimal |
88935.o1 | 88935bc2 | \([1, 1, 1, -3039275, -1515559858]\) | \(19827475353801179/5148111413025\) | \(806146982468832017475\) | \([2]\) | \(3870720\) | \(2.7206\) |
Rank
sage: E.rank()
The elliptic curves in class 88935bc have rank \(1\).
Complex multiplication
The elliptic curves in class 88935bc do not have complex multiplication.Modular form 88935.2.a.bc
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.