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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 246420.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 246420.h1 | 246420h2 | \([0, 0, 0, -148114848, 693818251828]\) | \(750484394082304/578125\) | \(276821353719828000000\) | \([]\) | \(17729280\) | \(3.2304\) | |
| 246420.h2 | 246420h1 | \([0, 0, 0, -2234208, 498628132]\) | \(2575826944/1266325\) | \(606349493187911251200\) | \([]\) | \(5909760\) | \(2.6810\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 246420.h have rank \(1\).
Complex multiplication
The elliptic curves in class 246420.h do not have complex multiplication.Modular form 246420.2.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.
