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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 66300.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66300.v1 | 66300m2 | \([0, -1, 0, -9508, 281512]\) | \(23767139536/5386875\) | \(21547500000000\) | \([2]\) | \(184320\) | \(1.2711\) | |
66300.v2 | 66300m1 | \([0, -1, 0, -3133, -62738]\) | \(13608288256/845325\) | \(211331250000\) | \([2]\) | \(92160\) | \(0.92457\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 66300.v have rank \(0\).
Complex multiplication
The elliptic curves in class 66300.v do not have complex multiplication.Modular form 66300.2.a.v
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.