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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 290145.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
290145.bc1 | 290145bc2 | \([0, 1, 1, -67631761986, 16750667144005445]\) | \(-2358271688914380083572736/6990657638957734060575\) | \(-101414490835683576360245288334264675\) | \([]\) | \(3455872000\) | \(5.4039\) | |
290145.bc2 | 290145bc1 | \([0, 1, 1, -3543567236, -142972044989905]\) | \(-339206185979506036736/412391078349609375\) | \(-5982617572763813134439326171875\) | \([]\) | \(691174400\) | \(4.5992\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 290145.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 290145.bc do not have complex multiplication.Modular form 290145.2.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 LMFDB 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 LMFDB labels.