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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 374790.dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 374790.dg1 | 374790dg4 | \([1, 0, 0, -4019326829290, -3101373279885602140]\) | \(8091210786191720043428023421942881/519704638304164343196791040\) | \(461239779527719452216099355387818240\) | \([2]\) | \(17836277760\) | \(5.9009\) | |
| 374790.dg2 | 374790dg3 | \([1, 0, 0, -1355620571370, 570428870743887012]\) | \(310433085028455460797438794210401/21262790278439255798609760000\) | \(18870804640445854456166756682526560000\) | \([4]\) | \(17836277760\) | \(5.9009\) | |
| 374790.dg3 | 374790dg2 | \([1, 0, 0, -266518810090, -42218533160849500]\) | \(2359050000960547954302631210081/497591244921371048032665600\) | \(441614061501089360695818528242073600\) | \([2, 2]\) | \(8918138880\) | \(5.5543\) | |
| 374790.dg4 | 374790dg1 | \([1, 0, 0, 36100551190, -3991837015576668]\) | \(5862664580088804686022644639/11149139324455378527191040\) | \(-9894902190436001763130406590218240\) | \([2]\) | \(4459069440\) | \(5.2077\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 374790.dg have rank \(0\).
Complex multiplication
The elliptic curves in class 374790.dg do not have complex multiplication.Modular form 374790.2.a.dg
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
