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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 12480b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12480.t4 | 12480b1 | \([0, -1, 0, 255839, 1791265]\) | \(7064514799444439/4094064000000\) | \(-1073234313216000000\) | \([2]\) | \(138240\) | \(2.1492\) | \(\Gamma_0(N)\)-optimal |
| 12480.t3 | 12480b2 | \([0, -1, 0, -1024161, 15359265]\) | \(453198971846635561/261896250564000\) | \(68654530707849216000\) | \([2]\) | \(276480\) | \(2.4958\) | |
| 12480.t2 | 12480b3 | \([0, -1, 0, -3416161, -2620405535]\) | \(-16818951115904497561/1592332281446400\) | \(-417420353587485081600\) | \([2]\) | \(414720\) | \(2.6985\) | |
| 12480.t1 | 12480b4 | \([0, -1, 0, -55844961, -160609351455]\) | \(73474353581350183614361/576510977802240\) | \(151128893764990402560\) | \([2]\) | \(829440\) | \(3.0451\) |
Rank
sage: E.rank()
The elliptic curves in class 12480b have rank \(1\).
Complex multiplication
The elliptic curves in class 12480b do not have complex multiplication.Modular form 12480.2.a.b
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
