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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 301530.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
301530.i1 | 301530i2 | \([1, 1, 0, -4357648, 3499101952]\) | \(61817763688666201/7333209600\) | \(1085578202359334400\) | \([2]\) | \(10948608\) | \(2.4861\) | |
301530.i2 | 301530i1 | \([1, 1, 0, -294928, 44977408]\) | \(19164920149081/5155061760\) | \(763134150491504640\) | \([2]\) | \(5474304\) | \(2.1395\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 301530.i have rank \(1\).
Complex multiplication
The elliptic curves in class 301530.i do not have complex multiplication.Modular form 301530.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.