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SageMath
E = EllipticCurve("jm1")
E.isogeny_class()
Elliptic curves in class 277200.jm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277200.jm1 | 277200jm3 | \([0, 0, 0, -74529075, -70163932750]\) | \(981281029968144361/522287841796875\) | \(24367861546875000000000000\) | \([2]\) | \(56623104\) | \(3.5626\) | |
| 277200.jm2 | 277200jm2 | \([0, 0, 0, -58491075, -171989194750]\) | \(474334834335054841/607815140625\) | \(28358223201000000000000\) | \([2, 2]\) | \(28311552\) | \(3.2161\) | |
| 277200.jm3 | 277200jm1 | \([0, 0, 0, -58473075, -172100452750]\) | \(473897054735271721/779625\) | \(36374184000000000\) | \([2]\) | \(14155776\) | \(2.8695\) | \(\Gamma_0(N)\)-optimal |
| 277200.jm4 | 277200jm4 | \([0, 0, 0, -42741075, -266693944750]\) | \(-185077034913624841/551466161890875\) | \(-25729205249180664000000000\) | \([2]\) | \(56623104\) | \(3.5626\) |
Rank
sage: E.rank()
The elliptic curves in class 277200.jm have rank \(0\).
Complex multiplication
The elliptic curves in class 277200.jm do not have complex multiplication.Modular form 277200.2.a.jm
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.
