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SageMath
E = EllipticCurve("dr1")
E.isogeny_class()
Elliptic curves in class 474320.dr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
474320.dr1 | 474320dr2 | \([0, -1, 0, -7567380, -10851363620]\) | \(-18330740176/8857805\) | \(-23158291257023484826880\) | \([]\) | \(34836480\) | \(2.9970\) | |
474320.dr2 | 474320dr1 | \([0, -1, 0, 733220, 181793900]\) | \(16674224/15125\) | \(-39543561329525792000\) | \([]\) | \(11612160\) | \(2.4477\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 474320.dr have rank \(0\).
Complex multiplication
The elliptic curves in class 474320.dr do not have complex multiplication.Modular form 474320.2.a.dr
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.