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SageMath
E = EllipticCurve("jl1")
E.isogeny_class()
Elliptic curves in class 383040.jl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
383040.jl1 | 383040jl4 | \([0, 0, 0, -51228012, -136194043984]\) | \(77799851782095807001/3092322318750000\) | \(590951997864345600000000\) | \([2]\) | \(37748736\) | \(3.3280\) | |
383040.jl2 | 383040jl2 | \([0, 0, 0, -8327532, 6389991344]\) | \(334199035754662681/101099003040000\) | \(19320320351577047040000\) | \([2, 2]\) | \(18874368\) | \(2.9814\) | |
383040.jl3 | 383040jl1 | \([0, 0, 0, -7590252, 8047691696]\) | \(253060782505556761/41184460800\) | \(7870473023835340800\) | \([2]\) | \(9437184\) | \(2.6348\) | \(\Gamma_0(N)\)-optimal |
383040.jl4 | 383040jl3 | \([0, 0, 0, 22776468, 42881204144]\) | \(6837784281928633319/8113766016106800\) | \(-1550564832245673413836800\) | \([2]\) | \(37748736\) | \(3.3280\) |
Rank
sage: E.rank()
The elliptic curves in class 383040.jl have rank \(0\).
Complex multiplication
The elliptic curves in class 383040.jl do not have complex multiplication.Modular form 383040.2.a.jl
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.