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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 44400h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44400.t2 | 44400h1 | \([0, -1, 0, 592, -8688]\) | \(1431644/2775\) | \(-44400000000\) | \([2]\) | \(27648\) | \(0.72760\) | \(\Gamma_0(N)\)-optimal |
44400.t1 | 44400h2 | \([0, -1, 0, -4408, -88688]\) | \(296071778/61605\) | \(1971360000000\) | \([2]\) | \(55296\) | \(1.0742\) |
Rank
sage: E.rank()
The elliptic curves in class 44400h have rank \(2\).
Complex multiplication
The elliptic curves in class 44400h do not have complex multiplication.Modular form 44400.2.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.