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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 224400cd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
224400.gw1 | 224400cd1 | \([0, 1, 0, -3401408, -2415652812]\) | \(68001744211490809/1022422500\) | \(65435040000000000\) | \([2]\) | \(4644864\) | \(2.3632\) | \(\Gamma_0(N)\)-optimal |
224400.gw2 | 224400cd2 | \([0, 1, 0, -3301408, -2564252812]\) | \(-62178675647294809/8362782148050\) | \(-535218057475200000000\) | \([2]\) | \(9289728\) | \(2.7098\) |
Rank
sage: E.rank()
The elliptic curves in class 224400cd have rank \(0\).
Complex multiplication
The elliptic curves in class 224400cd do not have complex multiplication.Modular form 224400.2.a.cd
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.