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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 129360.co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129360.co1 | 129360bl2 | \([0, -1, 0, -1372800, 45267552]\) | \(3462051528686/1993006125\) | \(164710371157694208000\) | \([2]\) | \(3354624\) | \(2.5688\) | |
129360.co2 | 129360bl1 | \([0, -1, 0, 342200, 5479552]\) | \(107245762628/62390625\) | \(-2578111244016000000\) | \([2]\) | \(1677312\) | \(2.2222\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 129360.co have rank \(1\).
Complex multiplication
The elliptic curves in class 129360.co do not have complex multiplication.Modular form 129360.2.a.co
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.