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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 76440.da
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76440.da1 | 76440bo2 | \([0, 1, 0, -5248600520, 63292670950368]\) | \(386965237776463086681532/182055746334444328125\) | \(7522924584623981548068144000000\) | \([2]\) | \(146657280\) | \(4.6189\) | |
76440.da2 | 76440bo1 | \([0, 1, 0, -2701530540, -53367209445600]\) | \(211072197308055014773168/3052652281946850375\) | \(31535495806294117099661472000\) | \([2]\) | \(73328640\) | \(4.2723\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 76440.da have rank \(1\).
Complex multiplication
The elliptic curves in class 76440.da do not have complex multiplication.Modular form 76440.2.a.da
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.