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SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 179520.ev
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179520.ev1 | 179520bi4 | \([0, 1, 0, -154710561, 556636714335]\) | \(1562225332123379392365961/393363080510106009600\) | \(103117771377241229780582400\) | \([2]\) | \(53084160\) | \(3.7014\) | |
| 179520.ev2 | 179520bi2 | \([0, 1, 0, -53118561, -148975050465]\) | \(63229930193881628103961/26218934428500000\) | \(6873136346824704000000\) | \([2]\) | \(17694720\) | \(3.1521\) | |
| 179520.ev3 | 179520bi1 | \([0, 1, 0, -2809441, -3068540641]\) | \(-9354997870579612441/10093752054144000\) | \(-2646016538481524736000\) | \([2]\) | \(8847360\) | \(2.8055\) | \(\Gamma_0(N)\)-optimal |
| 179520.ev4 | 179520bi3 | \([0, 1, 0, 23547359, 55411094879]\) | \(5508208700580085578359/8246033269590589440\) | \(-2161648145423555478159360\) | \([2]\) | \(26542080\) | \(3.3548\) |
Rank
sage: E.rank()
The elliptic curves in class 179520.ev have rank \(0\).
Complex multiplication
The elliptic curves in class 179520.ev do not have complex multiplication.Modular form 179520.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
