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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 304200h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
304200.h2 | 304200h1 | \([0, 0, 0, -53235, 2965950]\) | \(37044/13\) | \(5855189618304000\) | \([2]\) | \(1720320\) | \(1.7269\) | \(\Gamma_0(N)\)-optimal |
304200.h1 | 304200h2 | \([0, 0, 0, -357435, -80080650]\) | \(5606442/169\) | \(152234930075904000\) | \([2]\) | \(3440640\) | \(2.0734\) |
Rank
sage: E.rank()
The elliptic curves in class 304200h have rank \(0\).
Complex multiplication
The elliptic curves in class 304200h do not have complex multiplication.Modular form 304200.2.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.