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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 372810.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
372810.z1 | 372810z1 | \([1, 1, 0, -66042, 7417116]\) | \(-1319778683209/228159720\) | \(-5507220984520680\) | \([]\) | \(4603392\) | \(1.7466\) | \(\Gamma_0(N)\)-optimal |
372810.z2 | 372810z2 | \([1, 1, 0, 449823, -31685451]\) | \(417016893087431/259510848000\) | \(-6263960999848512000\) | \([]\) | \(13810176\) | \(2.2959\) |
Rank
sage: E.rank()
The elliptic curves in class 372810.z have rank \(1\).
Complex multiplication
The elliptic curves in class 372810.z do not have complex multiplication.Modular form 372810.2.a.z
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.