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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 35520dd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35520.ck3 | 35520dd1 | \([0, 1, 0, -12488865, -16991784225]\) | \(821774646379511057449/38361600000\) | \(10056263270400000\) | \([2]\) | \(1105920\) | \(2.5494\) | \(\Gamma_0(N)\)-optimal |
35520.ck2 | 35520dd2 | \([0, 1, 0, -12509345, -16933281057]\) | \(825824067562227826729/5613755625000000\) | \(1471612354560000000000\) | \([2, 2]\) | \(2211840\) | \(2.8959\) | |
35520.ck4 | 35520dd3 | \([0, 1, 0, -4837025, -37475150625]\) | \(-47744008200656797609/2286529541015625000\) | \(-599400000000000000000000\) | \([2]\) | \(4423680\) | \(3.2425\) | |
35520.ck1 | 35520dd4 | \([0, 1, 0, -20509345, 7353118943]\) | \(3639478711331685826729/2016912141902025000\) | \(528721416526764441600000\) | \([4]\) | \(4423680\) | \(3.2425\) |
Rank
sage: E.rank()
The elliptic curves in class 35520dd have rank \(1\).
Complex multiplication
The elliptic curves in class 35520dd do not have complex multiplication.Modular form 35520.2.a.dd
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.