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SageMath
E = EllipticCurve("fn1")
E.isogeny_class()
Elliptic curves in class 304200.fn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
304200.fn1 | 304200fn2 | \([0, 0, 0, -53235, 4723550]\) | \(1000188\) | \(16681451904000\) | \([2]\) | \(1105920\) | \(1.4565\) | |
304200.fn2 | 304200fn1 | \([0, 0, 0, -2535, 109850]\) | \(-432\) | \(-4170362976000\) | \([2]\) | \(552960\) | \(1.1100\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 304200.fn have rank \(0\).
Complex multiplication
The elliptic curves in class 304200.fn do not have complex multiplication.Modular form 304200.2.a.fn
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.