Show commands: SageMath
Rank
The elliptic curves in class 304200er have rank \(0\).
L-function data
Bad L-factors: |
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Good L-factors: |
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See L-function page for more information |
Complex multiplication
The elliptic curves in class 304200er do not have complex multiplication.Modular form 304200.2.a.er
Isogeny 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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
The vertices are labelled with Cremona labels.
Elliptic curves in class 304200er
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
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304200.er2 | 304200er1 | \([0, 0, 0, -1280175, -32185500750]\) | \(-445090032/858203125\) | \(-447377317298437500000000\) | \([2]\) | \(37158912\) | \(3.2171\) | \(\Gamma_0(N)\)-optimal |
304200.er1 | 304200er2 | \([0, 0, 0, -159717675, -767493938250]\) | \(216092050322508/3016755625\) | \(6290482983069870000000000\) | \([2]\) | \(74317824\) | \(3.5637\) |