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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 43560z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43560.cf1 | 43560z1 | \([0, 0, 0, -41382, -3126519]\) | \(379275264/15125\) | \(312535248498000\) | \([2]\) | \(184320\) | \(1.5478\) | \(\Gamma_0(N)\)-optimal |
43560.cf2 | 43560z2 | \([0, 0, 0, 18513, -11427966]\) | \(2122416/171875\) | \(-56824590636000000\) | \([2]\) | \(368640\) | \(1.8944\) |
Rank
sage: E.rank()
The elliptic curves in class 43560z have rank \(0\).
Complex multiplication
The elliptic curves in class 43560z do not have complex multiplication.Modular form 43560.2.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 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.