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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 74529j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
74529.j1 | 74529j1 | \([1, -1, 1, -349355, 63034066]\) | \(421875/91\) | \(1017140714400993273\) | \([2]\) | \(774144\) | \(2.1693\) | \(\Gamma_0(N)\)-optimal |
74529.j2 | 74529j2 | \([1, -1, 1, 768580, 383210650]\) | \(4492125/8281\) | \(-92559805010490387843\) | \([2]\) | \(1548288\) | \(2.5159\) |
Rank
sage: E.rank()
The elliptic curves in class 74529j have rank \(0\).
Complex multiplication
The elliptic curves in class 74529j do not have complex multiplication.Modular form 74529.2.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 Cremona 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 Cremona labels.