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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 1155.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1155.h1 | 1155j2 | \([0, 1, 1, -841, -9674]\) | \(-65860951343104/3493875\) | \(-3493875\) | \([]\) | \(432\) | \(0.32335\) | |
1155.h2 | 1155j1 | \([0, 1, 1, -1, -35]\) | \(-262144/509355\) | \(-509355\) | \([3]\) | \(144\) | \(-0.22596\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1155.h have rank \(1\).
Complex multiplication
The elliptic curves in class 1155.h do not have complex multiplication.Modular form 1155.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.