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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 88935k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88935.ba2 | 88935k1 | \([0, -1, 1, 1780959, 260032772]\) | \(7196694080651264/4502793796875\) | \(-390871720197697921875\) | \([]\) | \(3110400\) | \(2.6403\) | \(\Gamma_0(N)\)-optimal |
88935.ba1 | 88935k2 | \([0, -1, 1, -21088041, -42595901503]\) | \(-11947588428895092736/2118439154286675\) | \(-183894265143755556234075\) | \([]\) | \(9331200\) | \(3.1896\) |
Rank
sage: E.rank()
The elliptic curves in class 88935k have rank \(1\).
Complex multiplication
The elliptic curves in class 88935k do not have complex multiplication.Modular form 88935.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.