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SageMath
E = EllipticCurve("fi1")
E.isogeny_class()
Elliptic curves in class 360640fi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
360640.fi1 | 360640fi1 | \([0, 0, 0, -9212, 312816]\) | \(44851536/4025\) | \(7758433894400\) | \([2]\) | \(491520\) | \(1.2130\) | \(\Gamma_0(N)\)-optimal |
360640.fi2 | 360640fi2 | \([0, 0, 0, 10388, 1465296]\) | \(16078716/129605\) | \(-999286285598720\) | \([2]\) | \(983040\) | \(1.5596\) |
Rank
sage: E.rank()
The elliptic curves in class 360640fi have rank \(1\).
Complex multiplication
The elliptic curves in class 360640fi do not have complex multiplication.Modular form 360640.2.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.