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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 37905j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37905.o5 | 37905j1 | \([1, 1, 0, 25263, -957744]\) | \(37899197279/30541455\) | \(-1436849657496855\) | \([2]\) | \(161280\) | \(1.5963\) | \(\Gamma_0(N)\)-optimal |
| 37905.o4 | 37905j2 | \([1, 1, 0, -120942, -8472681]\) | \(4158523459441/1755191025\) | \(82574508094418025\) | \([2, 2]\) | \(322560\) | \(1.9429\) | |
| 37905.o3 | 37905j3 | \([1, 1, 0, -916947, 331739856]\) | \(1812322775712961/35919725625\) | \(1689875137306400625\) | \([2, 2]\) | \(645120\) | \(2.2894\) | |
| 37905.o2 | 37905j4 | \([1, 1, 0, -1664217, -826717086]\) | \(10835086336331041/4928904855\) | \(231884671268652255\) | \([2]\) | \(645120\) | \(2.2894\) | |
| 37905.o6 | 37905j5 | \([1, 1, 0, 30678, 985411581]\) | \(67867385039/8916370596525\) | \(-419478510036014163525\) | \([2]\) | \(1290240\) | \(2.6360\) | |
| 37905.o1 | 37905j6 | \([1, 1, 0, -14600652, 21467590599]\) | \(7316761561829228881/2961328125\) | \(139318290570703125\) | \([2]\) | \(1290240\) | \(2.6360\) |
Rank
sage: E.rank()
The elliptic curves in class 37905j have rank \(0\).
Complex multiplication
The elliptic curves in class 37905j do not have complex multiplication.Modular form 37905.2.a.j
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
