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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 416025h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
416025.h2 | 416025h1 | \([1, -1, 1, -355355, -3327478]\) | \(1860867/1075\) | \(2866836914019140625\) | \([2]\) | \(5677056\) | \(2.2312\) | \(\Gamma_0(N)\)-optimal* |
416025.h1 | 416025h2 | \([1, -1, 1, -3822230, 2867245022]\) | \(2315685267/9245\) | \(24654797460564609375\) | \([2]\) | \(11354112\) | \(2.5777\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 416025h have rank \(0\).
Complex multiplication
The elliptic curves in class 416025h do not have complex multiplication.Modular form 416025.2.a.h
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.