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SageMath
E = EllipticCurve("ji1")
E.isogeny_class()
Elliptic curves in class 273600.ji
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
273600.ji1 | 273600ji4 | \([0, 0, 0, -2196300, -1252762000]\) | \(784767874322/35625\) | \(53187840000000000\) | \([2]\) | \(4718592\) | \(2.2855\) | |
273600.ji2 | 273600ji3 | \([0, 0, 0, -684300, 201782000]\) | \(23735908082/1954815\) | \(2918523156480000000\) | \([2]\) | \(4718592\) | \(2.2855\) | |
273600.ji3 | 273600ji2 | \([0, 0, 0, -144300, -17458000]\) | \(445138564/81225\) | \(60634137600000000\) | \([2, 2]\) | \(2359296\) | \(1.9390\) | |
273600.ji4 | 273600ji1 | \([0, 0, 0, 17700, -1582000]\) | \(3286064/7695\) | \(-1436071680000000\) | \([2]\) | \(1179648\) | \(1.5924\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 273600.ji have rank \(1\).
Complex multiplication
The elliptic curves in class 273600.ji do not have complex multiplication.Modular form 273600.2.a.ji
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.