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SageMath
E = EllipticCurve("fi1")
E.isogeny_class()
Elliptic curves in class 145200fi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
145200.bt2 | 145200fi1 | \([0, -1, 0, -233933, 50699112]\) | \(-3196715008/649539\) | \(-287674490094750000\) | \([2]\) | \(1843200\) | \(2.0725\) | \(\Gamma_0(N)\)-optimal |
145200.bt1 | 145200fi2 | \([0, -1, 0, -3909308, 2976297612]\) | \(932410994128/29403\) | \(208356832332000000\) | \([2]\) | \(3686400\) | \(2.4190\) |
Rank
sage: E.rank()
The elliptic curves in class 145200fi have rank \(1\).
Complex multiplication
The elliptic curves in class 145200fi do not have complex multiplication.Modular form 145200.2.a.fi
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.