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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 262080h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
262080.h1 | 262080h1 | \([0, 0, 0, -2551188, 1568417888]\) | \(614983729942899136/35933625\) | \(107297229312000\) | \([2]\) | \(4177920\) | \(2.1570\) | \(\Gamma_0(N)\)-optimal |
262080.h2 | 262080h2 | \([0, 0, 0, -2546508, 1574458832]\) | \(-76450685425962632/587722078125\) | \(-14039429773824000000\) | \([2]\) | \(8355840\) | \(2.5036\) |
Rank
sage: E.rank()
The elliptic curves in class 262080h have rank \(1\).
Complex multiplication
The elliptic curves in class 262080h do not have complex multiplication.Modular form 262080.2.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.