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SageMath
E = EllipticCurve("nm1")
E.isogeny_class()
Elliptic curves in class 277200.nm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277200.nm1 | 277200nm2 | \([0, 0, 0, -4035, -76750]\) | \(77860436/17787\) | \(1659740544000\) | \([2]\) | \(294912\) | \(1.0573\) | |
277200.nm2 | 277200nm1 | \([0, 0, 0, -1335, 17750]\) | \(11279504/693\) | \(16166304000\) | \([2]\) | \(147456\) | \(0.71072\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277200.nm have rank \(1\).
Complex multiplication
The elliptic curves in class 277200.nm do not have complex multiplication.Modular form 277200.2.a.nm
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.