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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 1350.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1350.i1 | 1350d2 | \([1, -1, 0, -2742, -43084]\) | \(296595/64\) | \(492075000000\) | \([]\) | \(2160\) | \(0.95753\) | |
1350.i2 | 1350d1 | \([1, -1, 0, -867, 10041]\) | \(6838155/4\) | \(42187500\) | \([3]\) | \(720\) | \(0.40822\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1350.i have rank \(0\).
Complex multiplication
The elliptic curves in class 1350.i do not have complex multiplication.Modular form 1350.2.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.