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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2415.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2415.c1 | 2415h3 | \([1, 0, 0, -4430, -113505]\) | \(9614816895690721/34652610405\) | \(34652610405\) | \([2]\) | \(2048\) | \(0.88359\) | |
2415.c2 | 2415h2 | \([1, 0, 0, -405, 0]\) | \(7347774183121/4251692025\) | \(4251692025\) | \([2, 2]\) | \(1024\) | \(0.53702\) | |
2415.c3 | 2415h1 | \([1, 0, 0, -280, 1775]\) | \(2428257525121/8150625\) | \(8150625\) | \([4]\) | \(512\) | \(0.19044\) | \(\Gamma_0(N)\)-optimal |
2415.c4 | 2415h4 | \([1, 0, 0, 1620, 405]\) | \(470166844956479/272118787605\) | \(-272118787605\) | \([2]\) | \(2048\) | \(0.88359\) |
Rank
sage: E.rank()
The elliptic curves in class 2415.c have rank \(1\).
Complex multiplication
The elliptic curves in class 2415.c do not have complex multiplication.Modular form 2415.2.a.c
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.