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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 34320t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 34320.bw4 | 34320t1 | \([0, 1, 0, -91356, -14498100]\) | \(-329381898333928144/162600887109375\) | \(-41625827100000000\) | \([2]\) | \(344064\) | \(1.8942\) | \(\Gamma_0(N)\)-optimal |
| 34320.bw3 | 34320t2 | \([0, 1, 0, -1603856, -782243100]\) | \(445574312599094932036/61129333175625\) | \(62596437171840000\) | \([2, 2]\) | \(688128\) | \(2.2408\) | |
| 34320.bw2 | 34320t3 | \([0, 1, 0, -1746856, -634609900]\) | \(287849398425814280018/81784533026485575\) | \(167494723638242457600\) | \([2]\) | \(1376256\) | \(2.5873\) | |
| 34320.bw1 | 34320t4 | \([0, 1, 0, -25660856, -50041356300]\) | \(912446049969377120252018/17177299425\) | \(35179109222400\) | \([2]\) | \(1376256\) | \(2.5873\) |
Rank
sage: E.rank()
The elliptic curves in class 34320t have rank \(0\).
Complex multiplication
The elliptic curves in class 34320t do not have complex multiplication.Modular form 34320.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
