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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 205350.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
205350.l1 | 205350eb2 | \([1, 1, 0, -2415447200, -45693307776000]\) | \(62202232222815625/232783872\) | \(5832614531051520000000000\) | \([]\) | \(186157440\) | \(3.9674\) | |
205350.l2 | 205350eb1 | \([1, 1, 0, -41087825, -11108272875]\) | \(306163065625/175056768\) | \(4386208718083848750000000\) | \([]\) | \(62052480\) | \(3.4181\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 205350.l have rank \(1\).
Complex multiplication
The elliptic curves in class 205350.l do not have complex multiplication.Modular form 205350.2.a.l
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.