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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 212940.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 212940.h1 | 212940bg2 | \([0, 0, 0, -298623, -62012522]\) | \(3269383504/47775\) | \(43035643694534400\) | \([2]\) | \(1806336\) | \(1.9952\) | |
| 212940.h2 | 212940bg1 | \([0, 0, 0, -2028, -2634203]\) | \(-16384/53235\) | \(-2997125185869360\) | \([2]\) | \(903168\) | \(1.6486\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 212940.h have rank \(1\).
Complex multiplication
The elliptic curves in class 212940.h do not have complex multiplication.Modular form 212940.2.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.
