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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 19320.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19320.h1 | 19320q2 | \([0, -1, 0, -1296, -14580]\) | \(117636968738/20539575\) | \(42065049600\) | \([2]\) | \(18432\) | \(0.75845\) | |
| 19320.h2 | 19320q1 | \([0, -1, 0, -376, 2716]\) | \(5756278756/499905\) | \(511902720\) | \([2]\) | \(9216\) | \(0.41187\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19320.h have rank \(0\).
Complex multiplication
The elliptic curves in class 19320.h do not have complex multiplication.Modular form 19320.2.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.
