Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 102960.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102960.d1 | 102960y4 | \([0, 0, 0, -1460523, -679376662]\) | \(461552841274085284/111344805\) | \(83118451553280\) | \([2]\) | \(1179648\) | \(2.0486\) | |
102960.d2 | 102960y3 | \([0, 0, 0, -180723, 13293218]\) | \(874453074310084/403786706895\) | \(301425161550289920\) | \([2]\) | \(1179648\) | \(2.0486\) | |
102960.d3 | 102960y2 | \([0, 0, 0, -91623, -10532122]\) | \(455795194086736/6998159025\) | \(1306024429881600\) | \([2, 2]\) | \(589824\) | \(1.7021\) | |
102960.d4 | 102960y1 | \([0, 0, 0, -498, -453697]\) | \(-1171019776/7623061875\) | \(-88915393710000\) | \([2]\) | \(294912\) | \(1.3555\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.d have rank \(0\).
Complex multiplication
The elliptic curves in class 102960.d do not have complex multiplication.Modular form 102960.2.a.d
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.