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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 18150.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18150.i1 | 18150f2 | \([1, 1, 0, -5864025, 5446705125]\) | \(55025549689/192000\) | \(77812273803000000000\) | \([]\) | \(684288\) | \(2.6794\) | |
18150.i2 | 18150f1 | \([1, 1, 0, -373650, -82102500]\) | \(14235529/1080\) | \(437694040141875000\) | \([]\) | \(228096\) | \(2.1300\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18150.i have rank \(0\).
Complex multiplication
The elliptic curves in class 18150.i do not have complex multiplication.Modular form 18150.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.