Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 3700.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3700.c1 | 3700b2 | \([0, -1, 0, -300533, -63314063]\) | \(750484394082304/578125\) | \(2312500000000\) | \([]\) | \(10368\) | \(1.6803\) | |
| 3700.c2 | 3700b1 | \([0, -1, 0, -4533, -44063]\) | \(2575826944/1266325\) | \(5065300000000\) | \([]\) | \(3456\) | \(1.1310\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3700.c have rank \(0\).
Complex multiplication
The elliptic curves in class 3700.c do not have complex multiplication.Modular form 3700.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
