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SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 25200.ev
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25200.ev1 | 25200ei4 | \([0, 0, 0, -405075, -99224750]\) | \(157551496201/13125\) | \(612360000000000\) | \([2]\) | \(196608\) | \(1.8812\) | |
25200.ev2 | 25200ei2 | \([0, 0, 0, -27075, -1322750]\) | \(47045881/11025\) | \(514382400000000\) | \([2, 2]\) | \(98304\) | \(1.5346\) | |
25200.ev3 | 25200ei1 | \([0, 0, 0, -9075, 315250]\) | \(1771561/105\) | \(4898880000000\) | \([2]\) | \(49152\) | \(1.1881\) | \(\Gamma_0(N)\)-optimal |
25200.ev4 | 25200ei3 | \([0, 0, 0, 62925, -8252750]\) | \(590589719/972405\) | \(-45368527680000000\) | \([2]\) | \(196608\) | \(1.8812\) |
Rank
sage: E.rank()
The elliptic curves in class 25200.ev have rank \(0\).
Complex multiplication
The elliptic curves in class 25200.ev do not have complex multiplication.Modular form 25200.2.a.ev
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.