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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 2450.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2450.k1 | 2450l2 | \([1, -1, 0, -334532, 74557776]\) | \(-5745702166029/8192\) | \(-5903156224000\) | \([]\) | \(13104\) | \(1.7220\) | |
2450.k2 | 2450l1 | \([1, -1, 0, -107, -1849]\) | \(-189/2\) | \(-1441200250\) | \([]\) | \(1008\) | \(0.43951\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2450.k have rank \(0\).
Complex multiplication
The elliptic curves in class 2450.k do not have complex multiplication.Modular form 2450.2.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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.