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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 109520.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
109520.v1 | 109520k3 | \([0, -1, 0, -115544056, 478084235376]\) | \(16232905099479601/4052240\) | \(42585862896050831360\) | \([2]\) | \(9455616\) | \(3.1421\) | |
109520.v2 | 109520k4 | \([0, -1, 0, -115105976, 481888872560]\) | \(-16048965315233521/256572640900\) | \(-2696377141592078451097600\) | \([2]\) | \(18911232\) | \(3.4887\) | |
109520.v3 | 109520k1 | \([0, -1, 0, -1643256, 443859056]\) | \(46694890801/18944000\) | \(199086575993225216000\) | \([2]\) | \(3151872\) | \(2.5928\) | \(\Gamma_0(N)\)-optimal |
109520.v4 | 109520k2 | \([0, -1, 0, 5366024, 3225141360]\) | \(1625964918479/1369000000\) | \(-14387115843260416000000\) | \([2]\) | \(6303744\) | \(2.9394\) |
Rank
sage: E.rank()
The elliptic curves in class 109520.v have rank \(0\).
Complex multiplication
The elliptic curves in class 109520.v do not have complex multiplication.Modular form 109520.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.