Show commands:
SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 366912bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 366912.bh3 | 366912bh1 | \([0, 0, 0, 380436, -858833584]\) | \(270840023/14329224\) | \(-322165003890223742976\) | \([]\) | \(15925248\) | \(2.6148\) | \(\Gamma_0(N)\)-optimal |
| 366912.bh2 | 366912bh2 | \([0, 0, 0, -3429804, 23412395216]\) | \(-198461344537/10417365504\) | \(-234214399755495665565696\) | \([]\) | \(47775744\) | \(3.1641\) | |
| 366912.bh1 | 366912bh3 | \([0, 0, 0, -735419244, 7676400516176]\) | \(-1956469094246217097/36641439744\) | \(-823812202089182140563456\) | \([]\) | \(143327232\) | \(3.7134\) |
Rank
sage: E.rank()
The elliptic curves in class 366912bh have rank \(1\).
Complex multiplication
The elliptic curves in class 366912bh do not have complex multiplication.Modular form 366912.2.a.bh
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
