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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 30800.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30800.r1 | 30800bz4 | \([0, 1, 0, -1408008, 639087988]\) | \(4823468134087681/30382271150\) | \(1944465353600000000\) | \([2]\) | \(663552\) | \(2.3467\) | |
| 30800.r2 | 30800bz2 | \([0, 1, 0, -108008, -13112012]\) | \(2177286259681/105875000\) | \(6776000000000000\) | \([2]\) | \(221184\) | \(1.7974\) | |
| 30800.r3 | 30800bz3 | \([0, 1, 0, -36008, 21687988]\) | \(-80677568161/3131816380\) | \(-200436248320000000\) | \([2]\) | \(331776\) | \(2.0001\) | |
| 30800.r4 | 30800bz1 | \([0, 1, 0, 3992, -792012]\) | \(109902239/4312000\) | \(-275968000000000\) | \([2]\) | \(110592\) | \(1.4508\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30800.r have rank \(2\).
Complex multiplication
The elliptic curves in class 30800.r do not have complex multiplication.Modular form 30800.2.a.r
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
