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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 154128ca
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
154128.bk3 | 154128ca1 | \([0, -1, 0, -4112, 89088]\) | \(389017/57\) | \(1126924750848\) | \([2]\) | \(184320\) | \(1.0375\) | \(\Gamma_0(N)\)-optimal |
154128.bk2 | 154128ca2 | \([0, -1, 0, -17632, -808640]\) | \(30664297/3249\) | \(64234710798336\) | \([2, 2]\) | \(368640\) | \(1.3840\) | |
154128.bk4 | 154128ca3 | \([0, -1, 0, 22928, -4020992]\) | \(67419143/390963\) | \(-7729576866066432\) | \([2]\) | \(737280\) | \(1.7306\) | |
154128.bk1 | 154128ca4 | \([0, -1, 0, -274512, -55267200]\) | \(115714886617/1539\) | \(30426968272896\) | \([2]\) | \(737280\) | \(1.7306\) |
Rank
sage: E.rank()
The elliptic curves in class 154128ca have rank \(0\).
Complex multiplication
The elliptic curves in class 154128ca do not have complex multiplication.Modular form 154128.2.a.ca
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.