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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 53958v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53958.s2 | 53958v1 | \([1, 0, 1, -135171, -19132226]\) | \(1845026709625/793152\) | \(117414961432128\) | \([2]\) | \(285120\) | \(1.6599\) | \(\Gamma_0(N)\)-optimal |
53958.s3 | 53958v2 | \([1, 0, 1, -114011, -25319410]\) | \(-1107111813625/1228691592\) | \(-181890452128545288\) | \([2]\) | \(570240\) | \(2.0064\) | |
53958.s1 | 53958v3 | \([1, 0, 1, -397026, 72764596]\) | \(46753267515625/11591221248\) | \(1715916742043369472\) | \([2]\) | \(855360\) | \(2.2092\) | |
53958.s4 | 53958v4 | \([1, 0, 1, 957214, 461702324]\) | \(655215969476375/1001033261568\) | \(-148188848794788413952\) | \([2]\) | \(1710720\) | \(2.5557\) |
Rank
sage: E.rank()
The elliptic curves in class 53958v have rank \(0\).
Complex multiplication
The elliptic curves in class 53958v do not have complex multiplication.Modular form 53958.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.