Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 21294t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 21294.bh3 | 21294t1 | \([1, -1, 0, 20502, -10749348]\) | \(270840023/14329224\) | \(-50420867549971464\) | \([]\) | \(290304\) | \(1.8846\) | \(\Gamma_0(N)\)-optimal |
| 21294.bh2 | 21294t2 | \([1, -1, 0, -184833, 292941117]\) | \(-198461344537/10417365504\) | \(-36656039873256620544\) | \([]\) | \(870912\) | \(2.4339\) | |
| 21294.bh1 | 21294t3 | \([1, -1, 0, -39631968, 96043594752]\) | \(-1956469094246217097/36641439744\) | \(-128931837493257437184\) | \([]\) | \(2612736\) | \(2.9832\) |
Rank
sage: E.rank()
The elliptic curves in class 21294t have rank \(0\).
Complex multiplication
The elliptic curves in class 21294t do not have complex multiplication.Modular form 21294.2.a.t
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.
