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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 4400.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4400.h1 | 4400k2 | \([0, 1, 0, -228, 748]\) | \(41141648/14641\) | \(468512000\) | \([2]\) | \(1536\) | \(0.36476\) | |
4400.h2 | 4400k1 | \([0, 1, 0, -203, 1048]\) | \(464857088/121\) | \(242000\) | \([2]\) | \(768\) | \(0.018186\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4400.h have rank \(1\).
Complex multiplication
The elliptic curves in class 4400.h do not have complex multiplication.Modular form 4400.2.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.