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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 121275.dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121275.dn1 | 121275dz1 | \([0, 0, 1, -984900, 376217406]\) | \(-78843215872/539\) | \(-722311550296875\) | \([]\) | \(1036800\) | \(2.0320\) | \(\Gamma_0(N)\)-optimal |
| 121275.dn2 | 121275dz2 | \([0, 0, 1, -543900, 713858031]\) | \(-13278380032/156590819\) | \(-209846673903798421875\) | \([]\) | \(3110400\) | \(2.5813\) | |
| 121275.dn3 | 121275dz3 | \([0, 0, 1, 4858350, -18477635094]\) | \(9463555063808/115539436859\) | \(-154833895655013342796875\) | \([]\) | \(9331200\) | \(3.1306\) |
Rank
sage: E.rank()
The elliptic curves in class 121275.dn have rank \(0\).
Complex multiplication
The elliptic curves in class 121275.dn do not have complex multiplication.Modular form 121275.2.a.dn
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
