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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 222180.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
222180.z1 | 222180b1 | \([0, 1, 0, -245, -1512]\) | \(8388608/315\) | \(61321680\) | \([2]\) | \(73728\) | \(0.26292\) | \(\Gamma_0(N)\)-optimal |
222180.z2 | 222180b2 | \([0, 1, 0, 100, -5100]\) | \(35152/3675\) | \(-11446713600\) | \([2]\) | \(147456\) | \(0.60949\) |
Rank
sage: E.rank()
The elliptic curves in class 222180.z have rank \(0\).
Complex multiplication
The elliptic curves in class 222180.z do not have complex multiplication.Modular form 222180.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.