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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 2520.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2520.r1 | 2520t4 | \([0, 0, 0, -33627, 2373446]\) | \(5633270409316/14175\) | \(10581580800\) | \([2]\) | \(4096\) | \(1.1618\) | |
2520.r2 | 2520t3 | \([0, 0, 0, -5907, -127906]\) | \(30534944836/8203125\) | \(6123600000000\) | \([2]\) | \(4096\) | \(1.1618\) | |
2520.r3 | 2520t2 | \([0, 0, 0, -2127, 36146]\) | \(5702413264/275625\) | \(51438240000\) | \([2, 2]\) | \(2048\) | \(0.81521\) | |
2520.r4 | 2520t1 | \([0, 0, 0, 78, 2189]\) | \(4499456/180075\) | \(-2100394800\) | \([4]\) | \(1024\) | \(0.46863\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2520.r have rank \(1\).
Complex multiplication
The elliptic curves in class 2520.r do not have complex multiplication.Modular form 2520.2.a.r
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.