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SageMath
E = EllipticCurve("fi1")
E.isogeny_class()
Elliptic curves in class 238050.fi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
238050.fi1 | 238050fi2 | \([1, -1, 1, -93556130, -241204828503]\) | \(53706380371489/16171875000\) | \(27269360055867919921875000\) | \([2]\) | \(48660480\) | \(3.5859\) | |
238050.fi2 | 238050fi1 | \([1, -1, 1, 15946870, -25264912503]\) | \(265971760991/317400000\) | \(-535206640029834375000000\) | \([2]\) | \(24330240\) | \(3.2393\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 238050.fi have rank \(0\).
Complex multiplication
The elliptic curves in class 238050.fi do not have complex multiplication.Modular form 238050.2.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 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.