Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 378450w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 378450.w2 | 378450w1 | \([1, -1, 0, -193167, -11283770259]\) | \(-117649/8118144\) | \(-55003749093187614000000\) | \([]\) | \(26342400\) | \(3.0424\) | \(\Gamma_0(N)\)-optimal |
| 378450.w1 | 378450w2 | \([1, -1, 0, -1232047917, 16694216392491]\) | \(-30526075007211889/103499257854\) | \(-701249843601264468354468750\) | \([]\) | \(184396800\) | \(4.0153\) |
Rank
sage: E.rank()
The elliptic curves in class 378450w have rank \(0\).
Complex multiplication
The elliptic curves in class 378450w do not have complex multiplication.Modular form 378450.2.a.w
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
