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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 152592.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152592.h1 | 152592bm2 | \([0, -1, 0, -219810438424, 39666271783028464]\) | \(2418067440128989194388361/8359273562112\) | \(4060399619229184468916895744\) | \([2]\) | \(666796032\) | \(4.9414\) | |
| 152592.h2 | 152592bm1 | \([0, -1, 0, -13744282904, 619208105854704]\) | \(591139158854005457801/1097587482427392\) | \(533137689848843142208740655104\) | \([2]\) | \(333398016\) | \(4.5948\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152592.h have rank \(1\).
Complex multiplication
The elliptic curves in class 152592.h do not have complex multiplication.Modular form 152592.2.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.
