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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 190608.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
190608.h1 | 190608bj2 | \([0, -1, 0, -12204, -514836]\) | \(114489359728/9801\) | \(17209615104\) | \([2]\) | \(360960\) | \(1.0065\) | |
190608.h2 | 190608bj1 | \([0, -1, 0, -709, -9056]\) | \(-359661568/131769\) | \(-14460857136\) | \([2]\) | \(180480\) | \(0.65990\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 190608.h have rank \(0\).
Complex multiplication
The elliptic curves in class 190608.h do not have complex multiplication.Modular form 190608.2.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.