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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 2450.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2450.j1 | 2450o2 | \([1, -1, 0, -6827, -215419]\) | \(-5745702166029/8192\) | \(-50176000\) | \([]\) | \(1872\) | \(0.74903\) | |
2450.j2 | 2450o1 | \([1, -1, 0, -2, 6]\) | \(-189/2\) | \(-12250\) | \([]\) | \(144\) | \(-0.53344\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2450.j have rank \(1\).
Complex multiplication
The elliptic curves in class 2450.j do not have complex multiplication.Modular form 2450.2.a.j
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.