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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 30960.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30960.k1 | 30960bj2 | \([0, 0, 0, -73083, -7602518]\) | \(14457238157881/4437600\) | \(13250602598400\) | \([2]\) | \(92160\) | \(1.4948\) | |
30960.k2 | 30960bj1 | \([0, 0, 0, -3963, -151382]\) | \(-2305199161/1981440\) | \(-5916548136960\) | \([2]\) | \(46080\) | \(1.1482\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30960.k have rank \(0\).
Complex multiplication
The elliptic curves in class 30960.k do not have complex multiplication.Modular form 30960.2.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 LMFDB 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 LMFDB labels.