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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 36300.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
36300.h1 | 36300bc2 | \([0, -1, 0, -1295708, 417909912]\) | \(271593488/72171\) | \(63927664465500000000\) | \([2]\) | \(921600\) | \(2.5088\) | |
36300.h2 | 36300bc1 | \([0, -1, 0, -463833, -116153838]\) | \(199344128/9801\) | \(542595917531250000\) | \([2]\) | \(460800\) | \(2.1623\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 36300.h have rank \(2\).
Complex multiplication
The elliptic curves in class 36300.h do not have complex multiplication.Modular form 36300.2.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 LMFDB 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 LMFDB labels.