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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 300600i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
300600.i2 | 300600i1 | \([0, 0, 0, -60375, 9958250]\) | \(-8346562000/9861183\) | \(-28755209628000000\) | \([2]\) | \(2027520\) | \(1.8521\) | \(\Gamma_0(N)\)-optimal |
300600.i1 | 300600i2 | \([0, 0, 0, -1153875, 476882750]\) | \(14566408766500/6777027\) | \(79047242928000000\) | \([2]\) | \(4055040\) | \(2.1987\) |
Rank
sage: E.rank()
The elliptic curves in class 300600i have rank \(0\).
Complex multiplication
The elliptic curves in class 300600i do not have complex multiplication.Modular form 300600.2.a.i
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.