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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 301665.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
301665.ba1 | 301665ba2 | \([0, 1, 1, -233952671, -1377414784105]\) | \(-10272454218206642176/682489395\) | \(-94086958697636441355\) | \([]\) | \(39222144\) | \(3.2894\) | |
301665.ba2 | 301665ba1 | \([0, 1, 1, -2608571, -2270752090]\) | \(-14239618072576/7905184875\) | \(-1089796864655025583875\) | \([]\) | \(13074048\) | \(2.7401\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 301665.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 301665.ba do not have complex multiplication.Modular form 301665.2.a.ba
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.