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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 14450.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14450.j1 | 14450d2 | \([1, 0, 1, -9076, -334202]\) | \(-1723025/4\) | \(-191914062500\) | \([]\) | \(19200\) | \(1.0458\) | |
14450.j2 | 14450d1 | \([1, 0, 1, 104, 358]\) | \(1026895/1024\) | \(-125772800\) | \([]\) | \(3840\) | \(0.24110\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14450.j have rank \(1\).
Complex multiplication
The elliptic curves in class 14450.j do not have complex multiplication.Modular form 14450.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.